In this paper, we consider the problem of minimizing a strictly convex separable function over a feasible region defined by a convex inequality constraint and two-sided bounds on the variables (box constraints). Also, the convex separable program with a strictly convex objective function subject to linear equality constraints and bounded variables is considered. These problems are interesting f...

We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same Hessia...

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respe...

The introduction of a standard set of linear programming problems, to be found in NETLIB/LP/DATA, had an important impact on measuring, comparing and reporting the performance of LP solvers. Until recently the efficiency of new algorithmic developments has been measured using this important reference set. Presently, we are witnessing an ever growing interest in the area of quadratic programming...

We propose an adaptive, constraint-reduced, primal-dual interior-point algorithm for convex quadratic programming with many more inequality constraints than variables. We reduce the computational effort by assembling, instead of the exact normal-equation matrix, an approximate matrix from a well chosen index set which includes indices of constraints that seem to be most critical. Starting with ...

This paper presents a genetic algorithm method for solving convex quadratic bilevel programming problem. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, the bilevel convex quadratic problem is transformed into a single level problem by applying Kuhn-Tucker conditions, and then an effic...

Algorithms for projecting a point onto the intersection of convex sets are useful subroutines for solving optimization problems with constraints. One such algorithm is the Dykstra's algorithm, which is known to be alternating minimization on the dual problem. The projection onto each convex set generates a halfspace supporting the set. It is also relatively easy to project onto the intersection...

This paper addresses the problem of optimizing voltage profile radially-operated distribution systems by acting on active and reactive powers provided distributed energy resources (DERs). A novel optimization procedure is proposed adopting a decentralized control strategy. To this aim, centralized (VOP), minimizing distance all nodal voltages from their reference values, firstly formulated as s...