The ntd>mensiond veotor, &, 1s selected from E+-=I&. &bQ]. ,1 solution to P i s at hand hexh hen the solution to E satisfies the complementary alackness mnditlon gwen by. ?*#(?*) =&*bO and g(z*i s b 0 , ?\-here ?* eolves E far &=?* B n o o ~ s .WD C:EOFFAIOY'~' hare related this to the elsssical rork of K m m o Tucx~n's"" raddle-pomt erloivalenee by sholring thst. if &* exists, then (s? &'i 1s ...

Facets for the polyhedron of two-connected networks with bounded rings Abstract. We study the polyhedron associated with a network design problem which consists in determining at minimum cost a two-connected network such that the shortest cycle to which each edge belongs (a \ring") does not exceed a given length K. We present here a new formulation of the problem and derive facet results for di...

All numerals in this text are recycled. Preface Avoid reality at all costs — fortune() As the inclined reader will find out soon enough, this thesis is not about deeply involved mathematics as a mean in itself, but about how to apply mathematics to solve real-world problems. We will show how to shape, forge, and yield our tool of choice to rapidly answer questions of concern to people outside ...

Symmetry is mainly exploited in mathematical programming in order to reduce the computation times of enumerative algorithms. The most widespread approach rests on: (a) finding symmetries in the problem instance; (b) reformulating the problem so that it does not allow some of the symmetric optima; (c) solving the modified problem. Sometimes (b) and (c) are performed concurrently: the solution al...

Arising from research in the computer science community, constraint programming is a relatively new technique for solving optimization problems. For those familiar with mathematical programming, there are a number of language barriers that exist that make it difficult to understand the concepts of constraint programming. This paper, which assumes a minimal background in linear and integer progr...