Reformulations of mathematical programming problems as linear complementarity problems

A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are (i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and unrestricted variables, (ii.) Minimum Linear Complementarity Problem (MLCP) which is an LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized, (iii.) Second Minimum Linear Complementarity Problem (SMLCP) which is an MLCP but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value. A number of well known mathematical programming problems, namely quadratic programming (convex, nonconvex, pseudoconvex nonconvex), bilinear programming, game theory, zero-one integer programming, the fixed charge problem, absolute value programming, variable separable programming are reformulated as members of this family of four complementarity problems

An enumerative method for the solution of linear complementarity problems

In this report an enumerative method for the solution of the Linear Complementarity Problem (LCP) is presented. This algorithm completely processes the LCP, and does not require any particular property of the LCP to apply. That is the algorithm terminates after either finding all the solutions of an LCP or establishing that no solution exists. The method is extended to also process the Second Linear Complementarity Problem (SLCP), a problem which has been introduced to represent the general quadratic program involving unrestricted variables

A program to reorder and solve sparse unsymmetric linear systems using the envelope method

The envelope data structure and the Choleski based (bordering) method for the solution of symmetric sparse systems of linear equations have been extended by the authors to solve unsymmetric systems of linear equations. The data structures used in this general linear equation Solver and a set of FORTRAN 77 subroutines are described. Some test data (extracted from LP problems as basis matrices) together with experimental results are presented

A General Strategy to Endow Natural Fusion-protein-Derived Peptides with Potent Antiviral Activity

Fusion between the viral and target cell membranes is an obligatory step for the infectivity of all enveloped virus, and blocking this process is a clinically validated therapeutic strategy

A projected-gradient interior-point algorithm for complementarity problems

Interior-point algorithms are among the most efficient techniques for solving complementarity problems. In this paper, a procedure for globalizing interior-point algorithms by using the maximum stepsize is introduced. The algorithm combines exact or inexact interior-point and projected-gradient search techniques and employs a line-search procedure for the natural merit function associated with the complementarity problem. For linear problems, the maximum stepsize is shown to be acceptable if the Newton interior-point search direction is employed. Complementarity and optimization problems are discussed, for which the algorithm is able to process by either finding a solution or showing that no solution exists. A modification of the algorithm for dealing with infeasible linear complementarity problems is introduced which, in practice, employs only interior-point search directions. Computational experiments on the solution of complementarity problems and convex programming problems by the new algorithm are included.57445748

On the natural merit function for solving complementarity problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Complementarity problems may be formulated as nonlinear systems of equations with non-negativity constraints. The natural merit function is the sum of squares of the components of the system. Sufficient conditions are established which guarantee that stationary points are solutions of the complementarity problem. Algorithmic consequences are discussed.1301211223Portuguese Science and Technology Foundation [POCI/MAT/56704/2004]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Portuguese Science and Technology Foundation [POCI/MAT/56704/2004