Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis ...Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis of the algorithm; Analysis of the complexity bound on obtaining an approximate solution.展开更多
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the s...A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.展开更多
A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction ...A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.展开更多
In this paper, by analyzing the propositions of solution of the convex quadratic programming with nonnegative constraints, we propose a feasible decomposition method for constrained equations. Under mild conditions, t...In this paper, by analyzing the propositions of solution of the convex quadratic programming with nonnegative constraints, we propose a feasible decomposition method for constrained equations. Under mild conditions, the global convergence can be obtained. The method is applied to the complementary problems. Numerical results are also given to show the efficiency of the proposed method.展开更多
对电池特性的深刻认识是电池应用研究的重要基础,而弛豫时间分布(distribution of relaxation times,DRT)法是解析电池阻抗谱(electrochemical impedance spectroscopy,EIS)、提取电极过程动力学信息和电池建模的有效手段。然而,DRT函...对电池特性的深刻认识是电池应用研究的重要基础,而弛豫时间分布(distribution of relaxation times,DRT)法是解析电池阻抗谱(electrochemical impedance spectroscopy,EIS)、提取电极过程动力学信息和电池建模的有效手段。然而,DRT函数的求解是一个典型的不适定问题,经典的数值积分方法无法保证解的存在性或唯一性。首先采用分段线性插值近似连续的DRT函数;再通过正则化方法改善问题的不适定性,将DRT函数的求解归结为严格的凸二次规划(quadratic programming,QP)问题;进而运用有效集法(active set method,ASM)得到DRT函数的最优近似解。基于该方法解析液态金属电池的阻抗谱,并简要分析其内阻特性。研究结果表明:该方法为全局收敛,收敛速度快,计算精度高;得到的DRT函数近似解既精确、稳定,又具有明确的物理意义。在电池机理分析和建模中,该方法具有显著的潜在应用价值。展开更多
Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regressio...Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.展开更多
A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorith...A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.展开更多
基金This research supported partially by The National Natural Science Foundation of China-19771079 and 19601035State Key Laboratory of Scientific and Engineering Computing.
文摘Presents a regular splitting and potential reduction method for solving a quadratic programming problem with box constraints. Discussion on the regular splitting and potential reduction algorithm; Complexity analysis of the algorithm; Analysis of the complexity bound on obtaining an approximate solution.
基金the National Natural Science Foundation of China (No.19771079)and State Key Laboratory of Scientific and Engineering Computing
文摘A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
文摘A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.
基金Supported by the National Natural Science Foundation of China (No. 61072144)
文摘In this paper, by analyzing the propositions of solution of the convex quadratic programming with nonnegative constraints, we propose a feasible decomposition method for constrained equations. Under mild conditions, the global convergence can be obtained. The method is applied to the complementary problems. Numerical results are also given to show the efficiency of the proposed method.
文摘对电池特性的深刻认识是电池应用研究的重要基础,而弛豫时间分布(distribution of relaxation times,DRT)法是解析电池阻抗谱(electrochemical impedance spectroscopy,EIS)、提取电极过程动力学信息和电池建模的有效手段。然而,DRT函数的求解是一个典型的不适定问题,经典的数值积分方法无法保证解的存在性或唯一性。首先采用分段线性插值近似连续的DRT函数;再通过正则化方法改善问题的不适定性,将DRT函数的求解归结为严格的凸二次规划(quadratic programming,QP)问题;进而运用有效集法(active set method,ASM)得到DRT函数的最优近似解。基于该方法解析液态金属电池的阻抗谱,并简要分析其内阻特性。研究结果表明:该方法为全局收敛,收敛速度快,计算精度高;得到的DRT函数近似解既精确、稳定,又具有明确的物理意义。在电池机理分析和建模中,该方法具有显著的潜在应用价值。
基金supported by the National Natural Science Foundation of China grants(Nos.11101092,10971034)the Joint National Natural Science Foundation of China/Research Grants Council of Hong Kong grant(No.71061160506)the Research Grants Council of Hong Kong grants(Nos.CUHK414808 and CUHK414610).
文摘Mathematical programming problems with semi-continuous variables and cardinality constraint have many applications,including production planning,portfolio selection,compressed sensing and subset selection in regression.This class of problems can be modeled as mixed-integer programs with special structures and are in general NP-hard.In the past few years,based on new reformulations,approximation and relaxation techniques,promising exact and approximate methods have been developed.We survey in this paper these recent developments for this challenging class of mathematical programming problems.
文摘A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.
