This paper proposes a conic approximation algorithm for solving quadratic optimization problems with linearcomplementarity *** provide a conic reformulation and its dual for the original problem such that these three...
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This paper proposes a conic approximation algorithm for solving quadratic optimization problems with linearcomplementarity *** provide a conic reformulation and its dual for the original problem such that these three problems share the same optimal objective value. Moreover, we show that the conic reformulation problem is attainable when the original problem has a nonempty and bounded feasible domain. Since the conic reformulation is in general a hard problem, some conic relaxations are further considered. We offer a condition under which both the semidefinite relaxation and its dual problem become strictly feasible for finding a lower bound in polynomial time. For more general cases, by adaptively refining the outer approximation of the feasible set, we propose a conic approximation algorithm to identify an optimal solution or an -optimal solution of the original problem. A convergence proof is given under simple assumptions. Some computational results are included to illustrate the effectiveness of the proposed algorithm.
This paper aims to solve a class of quadratic programming with linear cornplementarity constraints (QPLCCs). We transit it to an equivalent quadratic programming with nonsmooth equation constraints, and partially pena...
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This paper aims to solve a class of quadratic programming with linear cornplementarity constraints (QPLCCs). We transit it to an equivalent quadratic programming with nonsmooth equation constraints, and partially penalize the problem by setting the nonsmooth equation constraints as the penalty term. And then, we apply the majorization approach to solve the penalty form. We prove that this partially penalty method is exact. At last, by solving a sequence of convex semismooth quadratic optimization problems with linearconstraints, the QPLCC is solved and the convergence analysis is obtained. Numerical results are displayed at the ending of this paper.
We propose an inference procedure for a class of estimators defined as the solutions to linear and convex quadratic programming problems in which the coefficients in both the objective function and the constraints of ...
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We propose an inference procedure for a class of estimators defined as the solutions to linear and convex quadratic programming problems in which the coefficients in both the objective function and the constraints of the problem are estimated from data and hence involve sampling error. We argue that the Karush-Kuhn-Tucker conditions that characterize the solutions to these programming problems can be treated as moment conditions;by doing so, we transform the problem of inference on the solution to a constrained optimization problem (which is non-standard) into one involving inference on inequalities with pre-estimated coefficients, which is better understood. Our approach is valid regardless of whether the problem has a unique solution or multiple solutions. We apply our method to various portfolio selection models, in which the confidence sets can be non-convex, lower-dimensional manifolds. (C) 2021 Elsevier B.V. All rights reserved.
This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm...
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This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm proposed by Fukushima et al. [Computational Optimization and Applications, 10 (1998), 5-34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported.
＜正＞In this paper,a sequential quadratic programming（SQP） algorithm for solving a stationary point of a kind of mathematical programs with linear complementarity constraints is proposed,The algorithm is a modifica...
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＜正＞In this paper,a sequential quadratic programming（SQP） algorithm for solving a stationary point of a kind of mathematical programs with linear complementarity constraints is proposed,The algorithm is a modification of the SQP algoritm proposed by by Fukushima,Luo and Pang（Computational Optimization and Applications 10,5-34,1998.）,it is based on a reformulation of complementarity condition as a system of *** each iteration,to generate the search directions,one quadratic programming and one system of equations needed to be solved,a line and curve search is used to yield the step *** suitable as-sumptions, the algorithm is proved to possess global and superlinear convergence.
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