In the DIMACS benchmark suite for the maximum clique problem, the best known solution for test C2000.9 is a 78 nodes clique; optimality is not proved. We present a 79 nodes clique emerged during the testing of a heuristic algorithm. Article Download View Short communication: a larger clique for a DIMACS test
We study the behavior of subgradient projection algorithms for the quasiconvex feasibility problem of finding a point x^* in R^n that satisfies the inequalities f_i(x^*) less or equal 0, for all i=1,2,…,m, where all functions are continuous and quasiconvex. We consider the consistent case when the solution set is nonempty. Since the Fenchel-Moreau subdifferential might … Read more
This paper first presents an improve cutting plane method for solving the linear programming problems, based on the primal simplex method with the current equivalent facet technique, in which the increment of objection function is allowed as a pivot variable to decide the search step size. We obtain a strong valid inequality from the objective … Read more
For a real world problem — transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand — we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost … Read more
In this paper a special step control problem is considered. The formulation of the problem uses a parameter to control the switching point. By using Taylor’s increment methods first and second order optimality conditions (in the sense of Pontryagin’s maximum principle) will be derived. Citation Preprint 2005-1, Department of Mathematics and Computer Science, Technical University … Read more
A wide variety of problems in global optimization, combinatorial optimization as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how … Read more
The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which convex transaction costs are incurred to rebalance an investment portfolio. In particular, we consider linear, piecewise linear, and quadratic transaction costs. The Markowitz framework of mean-variance efficiency … Read more
A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted … Read more
In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate piecewise structure and directional differentiability of both — the lower level equilibrium solution and objective integrant. We show almost sure convergence of optimal values, optimal solutions … Read more
See pdf file Citation Report No. DAMTP 2004/NA08 (year 2004), CMS Building, Wilberforce Road, Cambridge CB3 0WA, UK. Article Download View The NEWUOA software for unconstrained optimization without derivatives