In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These ...In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.展开更多
In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular functi...In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.展开更多
In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the converg...In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.展开更多
In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems.The proposed step sizes employ second-order information in ...In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems.The proposed step sizes employ second-order information in order to obtain faster gradient-type methods.Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of the objective function.A convergence analysis of the proposed algorithm is provided.Some numerical experiments are performed in order to compare the efficiency and effectiveness of the proposed methods with similar methods in the literature.Experimentally,it is observed that our proposals accelerate the gradient method at nearly no extra computational cost,which makes our proposal a good alternative to solve large-scale problems.展开更多
基金the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai (Grant No.06XPYQ52)the Shanghai Pujiang Program (Grant No.06PJ14039)
文摘In this paper, a new primal-dual interior-point algorithm for convex quadratic optimization （CQO） based on a kernel function is presented. The proposed function has some properties that are easy for checking. These properties enable us to improve the polynomial complexity bound of a large-update interior-point method （IPM） to O（√n log nlog n/e）, which is the currently best known polynomial complexity bound for the algorithm with the large-update method. Numerical tests were conducted to investigate the behavior of the algorithm with different parameters p, q and θ, where p is the growth degree parameter, q is the barrier degree of the kernel function and θ is the barrier update parameter.
基金Supported by Natural Science Foundation of Hubei Province of China (Grant No. 2008CDZ047)
文摘In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.
文摘In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.
基金supported in part by CONACYT(Mexico),Grants 258033,256126.
文摘In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems.The proposed step sizes employ second-order information in order to obtain faster gradient-type methods.Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of the objective function.A convergence analysis of the proposed algorithm is provided.Some numerical experiments are performed in order to compare the efficiency and effectiveness of the proposed methods with similar methods in the literature.Experimentally,it is observed that our proposals accelerate the gradient method at nearly no extra computational cost,which makes our proposal a good alternative to solve large-scale problems.
