In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem (P). The algorithm works by globally solving problem (P1) that is equivalent to problem (P), by utilizing linearizat...In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem (P). The algorithm works by globally solving problem (P1) that is equivalent to problem (P), by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained. The proposed algorithm is convergent to the global minimum of (P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming. Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems (P).展开更多
The semidefinite matrix completion(SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, S...The semidefinite matrix completion(SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm.展开更多
基金Foundation item: Supported by the National Natural Science Foundation of China(10671057) Supported by the Natural Science Foundation of Henan Institute of Science and Technology(06054)
文摘In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem (P). The algorithm works by globally solving problem (P1) that is equivalent to problem (P), by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained. The proposed algorithm is convergent to the global minimum of (P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming. Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems (P).
基金supported by National Natural Science Foundation of China(Grant Nos.11431002,71271021 and 11301022)the Fundamental Research Funds for the Central Universities of China(Grant No.2012YJS118)
文摘The semidefinite matrix completion(SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm.