In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem....In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.展开更多
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal proble...A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.展开更多
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.展开更多
In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global conv...In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradie...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman's step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.展开更多
For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a sm...For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.展开更多
In this papert a recursive quadratic programming algorithm is proposed andstudied.The line search functions used are Han's nondifferentiable penalty functionswith a second order penalty term. In order to avoid mar...In this papert a recursive quadratic programming algorithm is proposed andstudied.The line search functions used are Han's nondifferentiable penalty functionswith a second order penalty term. In order to avoid maratos effect,Fukushima's mixeddirection is used as the direction of line search.Finallyt we prove the global convergenceand the local second order convergence of the algorithm.展开更多
A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed....A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.展开更多
The methods employed in recent years to retrieve vector wind information from single-Doppler radar observation are reviewed briefly. These methods are based on a linearity hypothesis for the wind field, so the retriev...The methods employed in recent years to retrieve vector wind information from single-Doppler radar observation are reviewed briefly. These methods are based on a linearity hypothesis for the wind field, so the retrieved wind field is sometimes negatively affected by the non-linearity of wind. This paper proposes a new method based on a non-linear approximation technique. This method, which relies on the piecewise smooth property of the wind field and makes full use of the radar velocity data, is applied to two cases of the Huaihe River Basin Energy and Water Cycle Experiment (HUBEX) in 1998. Checked against the wind field observed by dual-Doppler radar, the retrieved wind field by the method presented in this paper yields a relatively accurate horizontal vector wind field with high resolution, as well as a reasonable estimate of the magnitude of vertical velocity.展开更多
The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is re...The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.展开更多
文摘In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
基金Supported by the National Natural Science Foundation of China（10571106） Supported by the Fundamental Research Funds for the Central Universities（10CX04044A）
文摘In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman's step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971118, 10701047 and 10901096the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010
文摘For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
文摘In this papert a recursive quadratic programming algorithm is proposed andstudied.The line search functions used are Han's nondifferentiable penalty functionswith a second order penalty term. In order to avoid maratos effect,Fukushima's mixeddirection is used as the direction of line search.Finallyt we prove the global convergenceand the local second order convergence of the algorithm.
基金project supported by the National Natural Science Foundation of China(Nos.10501009 and 60471039)the Natural Science Foundation of Guangxi Province(No.0728206)
文摘A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.
基金The authors would like to express their thanks to the GAME/HUBEX Project Office for assistance.
文摘The methods employed in recent years to retrieve vector wind information from single-Doppler radar observation are reviewed briefly. These methods are based on a linearity hypothesis for the wind field, so the retrieved wind field is sometimes negatively affected by the non-linearity of wind. This paper proposes a new method based on a non-linear approximation technique. This method, which relies on the piecewise smooth property of the wind field and makes full use of the radar velocity data, is applied to two cases of the Huaihe River Basin Energy and Water Cycle Experiment (HUBEX) in 1998. Checked against the wind field observed by dual-Doppler radar, the retrieved wind field by the method presented in this paper yields a relatively accurate horizontal vector wind field with high resolution, as well as a reasonable estimate of the magnitude of vertical velocity.
文摘The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.
