We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear co...We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.展开更多
This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimato...This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimator satisfies a fixed point equation.The convergence property of the proposed algorithm is established.Numerical studies are conducted to evaluate the finite sample performance of the proposed algorithm.展开更多
Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identific...Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.展开更多
The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in q...The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in quantum computing:how to efficiently perform search over continuous domains.While Grover’s algorithm has been a cornerstone in discrete quantum search with its well-known quadratic speedup[2],many real-world problems—ranging from high-dimensional optimization to spectral analysis of infinite dimensional operators—require searching over continuous,uncountably infinite solution spaces.展开更多
A novel quantum search algorithm tailored for continuous optimization and spectral problems was proposed recently by a research team from the University of Electronic Science and Technology of China to broaden quantum...A novel quantum search algorithm tailored for continuous optimization and spectral problems was proposed recently by a research team from the University of Electronic Science and Technology of China to broaden quantum computation frontiers and enrich its application landscape.Quantum computing has traditionally excelled at tackling discrete search challenges,but many important applications from large-scale optimization to advanced physics simulations necessitate searching through continuous domains.These continuous search problems involve uncountably infinite solution spaces and bring about computational complexities far beyond those faced in conventional discrete settings.This draft,titled“Fixed-Point Quantum Continuous Search Algorithm with Optimal Query Complexity”,takes on the core challenge of performing search tasks in domains that may be uncountably infinite,offering theoretical and practical insights into achieving quantum speedups in such settings[1].展开更多
文摘We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.
基金Supported by the National Natural Science Foundation of China(11701571)
文摘This paper concerns computational problems of the concave penalized linear regression model.We propose a fixed point iterative algorithm to solve the computational problem based on the fact that the penalized estimator satisfies a fixed point equation.The convergence property of the proposed algorithm is established.Numerical studies are conducted to evaluate the finite sample performance of the proposed algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11401124 and 71271021)the Scientific Research Projects for the Introduced Talents of Guizhou University(Grant No.201343)the Key Program of National Natural Science Foundation of China(Grant No.11431002)
文摘Regularized minimization problems with nonconvex, nonsmooth, even non-Lipschitz penalty functions have attracted much attention in recent years, owing to their wide applications in statistics, control,system identification and machine learning. In this paper, the non-Lipschitz ?_p(0 < p < 1) regularized matrix minimization problem is studied. A global necessary optimality condition for this non-Lipschitz optimization problem is firstly obtained, specifically, the global optimal solutions for the problem are fixed points of the so-called p-thresholding operator which is matrix-valued and set-valued. Then a fixed point iterative scheme for the non-Lipschitz model is proposed, and the convergence analysis is also addressed in detail. Moreover,some acceleration techniques are adopted to improve the performance of this algorithm. The effectiveness of the proposed p-thresholding fixed point continuation(p-FPC) algorithm is demonstrated by numerical experiments on randomly generated and real matrix completion problems.
文摘The paper“Fixed-point quantum continuous search algorithm with optimal query complexity”[1]presents another interesting application of quantum search algorithms by addressing one of the long-standing challenges in quantum computing:how to efficiently perform search over continuous domains.While Grover’s algorithm has been a cornerstone in discrete quantum search with its well-known quadratic speedup[2],many real-world problems—ranging from high-dimensional optimization to spectral analysis of infinite dimensional operators—require searching over continuous,uncountably infinite solution spaces.
文摘A novel quantum search algorithm tailored for continuous optimization and spectral problems was proposed recently by a research team from the University of Electronic Science and Technology of China to broaden quantum computation frontiers and enrich its application landscape.Quantum computing has traditionally excelled at tackling discrete search challenges,but many important applications from large-scale optimization to advanced physics simulations necessitate searching through continuous domains.These continuous search problems involve uncountably infinite solution spaces and bring about computational complexities far beyond those faced in conventional discrete settings.This draft,titled“Fixed-Point Quantum Continuous Search Algorithm with Optimal Query Complexity”,takes on the core challenge of performing search tasks in domains that may be uncountably infinite,offering theoretical and practical insights into achieving quantum speedups in such settings[1].
