Maximum Clique Problem(MCP) is one of the 21 original NP -complete problems enumerated by Karp[19] in 1972. In the last years a large number of exact methods to solve MCP have been appeared[2, 3, 6, 8, 9, 13, 14,17,18,21,23,25,29-31,34-38,40-43]. Most of them are branch and bound algorithms and use branching rule introduced by Balas and Yu[3] and based on coloring heuristics to establish an upp...

We treat with tools from convex analysis the general problem of cutting planes, separating a point from a (closed convex) set P . Crucial for this is the computation of extreme points in the so-called reverse polar set, introduced by E. Balas in 1979. In the polyhedral case, this enables the computation of cuts that define facets of P . We exhibit three (equivalent) optimization problems to com...

This paper presents a comparative study of three Linear Parameter Varying (LPV) modeling approaches and their application to the longitudinal motion of a Boeing 747 series 100/200. The three approaches used to obtain the quasi-LPV models are Jacobian linearisation, state transformation, and function substitution. Development of linear parameter varying models are a key step in applying LPV cont...

Consider the following restricted (symmetric or asymmetric) traveling salesman problem: given an initial ordering of the n cities and an integer k > 0, nd a minimum cost tour such that if city i precedes city j by at least k positions in the initial ordering, then city i precedes city j in any optimal tour. Balas [5] has proposed a dynamic programming algorithm that solves this problem in time ...

A Literatura Brasileira contemporânea constitui-se como um campo discursivo plural e heterogêneo do qual emergem vozes subalternizadas historicamente pelo poder colonial. Nesse cenário, destaca-se a obra de Conceição Evaristo que, em seu fazer literário, vocaliza as vivências da mulher negra periférica projetada “escrevivência”, isto é, articulação experiência vivida pela escritora, pelos que c...

Maklum balas tambahan merupakan salah satu kaedah terbaik yang boleh digunakan untuk menjadikan proses pembelajaran motor menjadi lebih menarik dan berkesan. Kajian ini dijalankan mengkaji kesan maklum tambahan; maklumat kesalahan perlakuan (E), cara memperbaiki (C) gabungan tersebut (EC) terhadap ketepatan panahan kepada dua kumpulan pemanah mempunyai tahap penguasaan kemahiran berbeza (beginn...

Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection cut by formulating a system of polynomi...

Disjunctive cuts for Mixed-Integer Linear Programs have been introduced by Egon Balas in the late 70’s, and successfully exploited in practice since the late 90’s. In this paper we investigate the main ingredients of a disjunctive cut separation procedure, and analyze their impact on the quality of the root-node bound for a set of instances taken from MIPLIB library. We compare alternative norm...