First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking...First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.展开更多
Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stocha...Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.展开更多
We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for exampl...We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for example,the existence of solutions of the VIP and the monotonicity of the multivalued vector field,we prove that the sequence of the iterates given by the method converges to a solution of the problem.Furthermore,this convergence is linear or superlinear with respect to the Bregman distance.展开更多
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical ...Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.展开更多
The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including sat...The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an ...In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an exact penalty function as the merit function to determine if the trial step is accepted.The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an-stationary point is analyzed.We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition.Numerical results demonstrate that,compared to the state-of-the-art algorithms,SQP-PG is an effective method for equality constrained composite optimization problems.展开更多
A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that gov...A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.展开更多
In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by...In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem.We also present an application of the method to demand theory in economy.展开更多
This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method ...This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework.Convergence results are established without additional assumptions.And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.展开更多
In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiograp...In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis,so that the density of the whole object can be recovered layer by layer.Considering the relationship between different layers,we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results.In view of the anisotropy of classical discrete total variations,a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model.Furthermore,considering that the object density consists of continually changing parts and jumps,a high-order regularization term is introduced.The final hybrid regularization model is solved using the alternating proximal gradient method,which was recently applied in image processing.Density reconstruction results are presented for simulated radiographs,which shows that the proposed method has led to an improvement in terms of the preservation of edge location.展开更多
The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can b...The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.展开更多
In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective func...In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.展开更多
The problem of nonconvex and nonsmooth optimization(NNO)has been extensively studied in the machine learning community,leading to the development of numerous fast and convergent numerical algorithms.Existing algorithm...The problem of nonconvex and nonsmooth optimization(NNO)has been extensively studied in the machine learning community,leading to the development of numerous fast and convergent numerical algorithms.Existing algorithms typically employ unified iteration schemes and require explicit solutions to subproblems for ensuring convergence.However,these inflexible iteration schemes overlook task-specific details and may encounter difficulties in providing explicit solutions to subproblems.In contrast,there is evidence suggesting that practical applications can benefit from approximately solving subproblems;however,many existing works fail to establish the theoretical validity of such approximations.In this paper,the authors propose a hybrid inexact proximal alternating method(hiPAM),which addresses a general NNO problem with coupled terms while overcoming all aforementioned challenges.The proposed hiPAM algorithm offers a flexible yet highly efficient approach by seamlessly integrating any efficient methods for approximate subproblem solving that cater to specificities.Additionally,the authors have devised a simple yet implementable stopping criterion that generates a Cauchy sequence and ultimately converges to a critical point of the original NNO problem.The proposed numerical experiments using both simulated and real data have demonstrated that hiPAM represents an exceedingly efficient and robust approach to NNO problems.展开更多
We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping,regularized by the sum of both l1-norm a...We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping,regularized by the sum of both l1-norm and l2-norm of the optimization variables.This class of problems arise naturally from applications in sparse group Lasso,which is a popular technique for variable selection.An effective approach to solve such problems is by the Proximal Gradient Method(PGM).In this paper we prove a local error bound around the optimal solution set for this problem and use it to establish the linear convergence of the PGM method without assuming strong convexity of the overall objective function.展开更多
In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under na...In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.展开更多
In this paper,we address the issue of peak-to-average power ratio(PAPR)reduction in large-scale multiuser multiple-input multiple-output(MU-MIMO)orthogonal frequency-division multiplexing(OFDM)systems.PAPR reduction a...In this paper,we address the issue of peak-to-average power ratio(PAPR)reduction in large-scale multiuser multiple-input multiple-output(MU-MIMO)orthogonal frequency-division multiplexing(OFDM)systems.PAPR reduction and the multiuser interference(MUI)cancellation problem are jointly formulated as an l_(∞)-norm based composite convex optimization problem,which can be solved efficiently using the iterative proximal gradient method.The proximal operator associated with l_(∞)-norm is evaluated using a low-cost sorting algorithm.The proposed method adaptively chooses the step size to accelerate convergence.Simulation results reveal that the proximal gradient method converges swiftly while provid-ing considerable PAPR reduction and lower out-of-band radiation.展开更多
In this paper,we propose an inexact proximal point method to solve equilibrium problems using proximal distances and the diagonal subdifferential.Under some natural assumptions on the problem and the quasimonotonicit...In this paper,we propose an inexact proximal point method to solve equilibrium problems using proximal distances and the diagonal subdifferential.Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction,we prove that the sequence generated by the method converges to a solution point of the problem.展开更多
Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such mi...Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.展开更多
In this paper,we propose a modified proximal gradient method for solving a class of nonsmooth convex optimization problems,which arise in many contemporary statistical and signal processing applications.The proposed m...In this paper,we propose a modified proximal gradient method for solving a class of nonsmooth convex optimization problems,which arise in many contemporary statistical and signal processing applications.The proposed method adopts a new scheme to construct the descent direction based on the proximal gradient method.It is proven that the modified proximal gradient method is Q-linearly convergent without the assumption of the strong convexity of the objective function.Some numerical experiments have been conducted to evaluate the proposed method eventually.展开更多
文摘First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes applied to infinite-dimensional elliptic optimal control problems and to validate the theoretical estimates.
文摘Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.
文摘We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for example,the existence of solutions of the VIP and the monotonicity of the multivalued vector field,we prove that the sequence of the iterates given by the method converges to a solution of the problem.Furthermore,this convergence is linear or superlinear with respect to the Bregman distance.
文摘Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.
基金The work was supported by the National Natural Science Foundation of China(No.11571171)。
文摘The problem of correcting simultaneously mass and stiffness matrices of finite element model of undamped structural systems using vibration tests is considered in this paper.The desired matrix properties,including satisfaction of the characteristic equation,symmetry,positive semidefiniteness and sparsity,are imposed as side constraints to form the optimal matrix pencil approximation problem.Using partial Lagrangian multipliers,we transform the nonlinearly constrained optimization problem into an equivalent matrix linear variational inequality,develop a proximal point-like method for solving the matrix linear variational inequality,and analyze its global convergence.Numerical results are included to illustrate the performance and application of the proposed method.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
基金supported by the National Natural Science Foundation of China(Grant No.72394365).
文摘In this paper,we present an SQP-type proximal gradient method(SQP-PG)for composite optimization problems with equality constraints.At each iteration,SQP-PG solves a subproblem to get the search direction,and takes an exact penalty function as the merit function to determine if the trial step is accepted.The global convergence of the SQP-PG method is proved and the iteration complexity for obtaining an-stationary point is analyzed.We also establish the local linear convergence result of the SQP-PG method under the second-order sufficient condition.Numerical results demonstrate that,compared to the state-of-the-art algorithms,SQP-PG is an effective method for equality constrained composite optimization problems.
文摘A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-in-time, tracking functionals and its L2- and L1-costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.
文摘In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem.We also present an application of the method to demand theory in economy.
基金supported by the National Natural Science Foundation of China(No.61373174).
文摘This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable structures.The methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction framework.Convergence results are established without additional assumptions.And the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.
基金supported by National Postdoctoral Program for Innovative Talents(BX201700038)supported by NSFC(11571003)+1 种基金supported by NSFC(11675021)supported by Beijing Natural Science Foundation(Z180002)。
文摘In this paper,we consider 3 D tomographic reconstruction for axially symmetric objects from a single radiograph formed by cone-beam X-rays.All contemporary density reconstruction methods in high-energy X-ray radiography are based on the assumption that the cone beam can be treated as fan beams located at parallel planes perpendicular to the symmetric axis,so that the density of the whole object can be recovered layer by layer.Considering the relationship between different layers,we undertake the cone-beam global reconstruction to solve the ambiguity effect at the material interfaces of the reconstruction results.In view of the anisotropy of classical discrete total variations,a new discretization of total variation which yields sharp edges and has better isotropy is introduced in our reconstruction model.Furthermore,considering that the object density consists of continually changing parts and jumps,a high-order regularization term is introduced.The final hybrid regularization model is solved using the alternating proximal gradient method,which was recently applied in image processing.Density reconstruction results are presented for simulated radiographs,which shows that the proposed method has led to an improvement in terms of the preservation of edge location.
基金supported by the National Natural Science Foundation of China(No.61271014)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301110003)the Graduated Students Innovation Fund of Hunan Province(No.CX2012B238)
文摘The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.
文摘In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.
基金supported by the National Key R&D Program of China under Grant No.2023YFA1011303the National Natural Science Foundation of China under Grant Nos.61806057 and 12301479+1 种基金the China Postdoctoral Science Foundation under Grant No.2018M632018the Natural Science Foundation of Liaoning Province under Grant No.2023-MS-126。
文摘The problem of nonconvex and nonsmooth optimization(NNO)has been extensively studied in the machine learning community,leading to the development of numerous fast and convergent numerical algorithms.Existing algorithms typically employ unified iteration schemes and require explicit solutions to subproblems for ensuring convergence.However,these inflexible iteration schemes overlook task-specific details and may encounter difficulties in providing explicit solutions to subproblems.In contrast,there is evidence suggesting that practical applications can benefit from approximately solving subproblems;however,many existing works fail to establish the theoretical validity of such approximations.In this paper,the authors propose a hybrid inexact proximal alternating method(hiPAM),which addresses a general NNO problem with coupled terms while overcoming all aforementioned challenges.The proposed hiPAM algorithm offers a flexible yet highly efficient approach by seamlessly integrating any efficient methods for approximate subproblem solving that cater to specificities.Additionally,the authors have devised a simple yet implementable stopping criterion that generates a Cauchy sequence and ultimately converges to a critical point of the original NNO problem.The proposed numerical experiments using both simulated and real data have demonstrated that hiPAM represents an exceedingly efficient and robust approach to NNO problems.
基金This work was partially supported by the National Natural Science Foundation of China(Nos.61179033,DMS-1015346)。
文摘We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping,regularized by the sum of both l1-norm and l2-norm of the optimization variables.This class of problems arise naturally from applications in sparse group Lasso,which is a popular technique for variable selection.An effective approach to solve such problems is by the Proximal Gradient Method(PGM).In this paper we prove a local error bound around the optimal solution set for this problem and use it to establish the linear convergence of the PGM method without assuming strong convexity of the overall objective function.
基金Coordenação de Aperfeiçoamento de Pessoal de Nível Superior of the Federal University of Rio de Janeiro(UFRJ),Brazil.
文摘In this paper,we present an analysis about the rate of convergence of an inexact proximal point algorithm to solve minimization problems for quasiconvex objective functions on Hadamard manifolds.We prove that under natural assumptions the sequence generated by the algorithm converges linearly or superlinearly to a critical point of the problem.
文摘In this paper,we address the issue of peak-to-average power ratio(PAPR)reduction in large-scale multiuser multiple-input multiple-output(MU-MIMO)orthogonal frequency-division multiplexing(OFDM)systems.PAPR reduction and the multiuser interference(MUI)cancellation problem are jointly formulated as an l_(∞)-norm based composite convex optimization problem,which can be solved efficiently using the iterative proximal gradient method.The proximal operator associated with l_(∞)-norm is evaluated using a low-cost sorting algorithm.The proposed method adaptively chooses the step size to accelerate convergence.Simulation results reveal that the proximal gradient method converges swiftly while provid-ing considerable PAPR reduction and lower out-of-band radiation.
基金the E.A.Papa Quiroz was supported by the Postdoctoral Scholarship CAPES-Fundação de AmparoàPesquisa do Estado do Rio de Janeiro(No.EditalPAPD-2011)P.R.Oliveira’s research was partially supported by Conselho Nacional de Desemvolvimento Científico e Tecnológico.
文摘In this paper,we propose an inexact proximal point method to solve equilibrium problems using proximal distances and the diagonal subdifferential.Under some natural assumptions on the problem and the quasimonotonicity condition on the bifunction,we prove that the sequence generated by the method converges to a solution point of the problem.
文摘Consider the problem of minimizing the sum of two convex functions,one being smooth and the other non-smooth.In this paper,we introduce a general class of approximate proximal splitting(APS)methods for solving such minimization problems.Methods in the APS class include many well-known algorithms such as the proximal splitting method,the block coordinate descent method(BCD),and the approximate gradient projection methods for smooth convex optimization.We establish the linear convergence of APS methods under a local error bound assumption.Since the latter is known to hold for compressive sensing and sparse group LASSO problems,our analysis implies the linear convergence of the BCD method for these problems without strong convexity assumption.
基金the National Natural Science Foundation of China(No.61179033).
文摘In this paper,we propose a modified proximal gradient method for solving a class of nonsmooth convex optimization problems,which arise in many contemporary statistical and signal processing applications.The proposed method adopts a new scheme to construct the descent direction based on the proximal gradient method.It is proven that the modified proximal gradient method is Q-linearly convergent without the assumption of the strong convexity of the objective function.Some numerical experiments have been conducted to evaluate the proposed method eventually.
