A successive linear approximation algorithm for the global minimization of a concave quadratic program

Abstract

In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.

On–Off Scheduling for Electric Vehicle Charging in Two-Links Charging Stations Using Binary Optimization Approaches

“…SLA [5] is based on a concept similar to that of the FA algorithm. In this approach, the BQP problem given by ( 30) is reformulated as follows:…”

“…To address this, we analyze three computational algorithms-Frank-Wolfe (FW) [4], successive linear approximations (SLA) [5], and SLA with gradient descent updates. In the first case, the gradient of the objective function was minimized.…”

New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

“…In [37], the algorithm presented in [7] is generalized in order to handle concave quadratic problems, where the matrix of the quadratic function is negative semidefinite, the linear constraints are of equality and/or inequality type and the variables are bounded with bounds which can be finite or infinite.…”

“…After that, the current point is improved by using the global optimality criterion proposed in [18] or [34]. Recently in [37], the algorithm proposed in [7] is adapted for solving quadratic programs with a negative semidefinite matrix, subject to linear equality and inequality constraints, and the variables are bounded with finite or infinite bounds.…”

“…In this work, we generalize the algorithms proposed in [7,11,37] for solving nonconvex quadratic programming problems written in general form. Hence a new approach called "Successive Linear Programming Algorithm (SLPA)" is proposed.…”