In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of th...In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.展开更多
In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a ste...In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.展开更多
In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for t...In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.展开更多
This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complement...This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complementarity Problem) function, which can be further carry on the smoothing processing by aggregate function. Therefore, the original combinatorial optimization problem could be transformed into a general differential nonlinear programming problem, which can be solved by mature optimization technique. Through some numerical experiments, the applicability, robustness, and solution quality of the approach are proved, which could be applied to large scale problems.展开更多
In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the...In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.展开更多
This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization mo...This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.展开更多
文摘In this paper, an alternating direction nonmonotone approximate Newton algorithm (ADNAN) based on nonmonotone line search is developed for solving inverse problems. It is shown that ADNAN converges to a solution of the inverse problems and numerical results provide the effectiveness of the proposed algorithm.
文摘In this paper, we give a smoothing neural network algorithm for absolute value equations (AVE). By using smoothing function, we reformulate the AVE as a differentiable unconstrained optimization and we establish a steep descent method to solve it. We prove the stability and the equilibrium state of the neural network to be a solution of the AVE. The numerical tests show the efficient of the proposed algorithm.
文摘In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem.
文摘This paper presents a continuous method for solving binary quadratic programming problems. First, the original problem is converted into an equivalent continuous optimization problem by using NCP (Nonlinear Complementarity Problem) function, which can be further carry on the smoothing processing by aggregate function. Therefore, the original combinatorial optimization problem could be transformed into a general differential nonlinear programming problem, which can be solved by mature optimization technique. Through some numerical experiments, the applicability, robustness, and solution quality of the approach are proved, which could be applied to large scale problems.
文摘In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm.
文摘This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.
