In this paper we develop a new version of the algortihm proposed in [17] for solving exactly some variants of (un)weighted constrained two-dimensional cutting stock problems. We introduce one-dimensional bounded knapsacks in order to obtain an improved initial lower bound for limitating...

Semi-definite programming (SDP) is of growing importance in various filed: system control, mechanics, combinatorial optimization, ... Usually, it is solved by interior point methods, which are elegant, efficicent and well-suited. However, they have limitations, particularly in large-scale or...

We establish, in infinite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our...

In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub) optimal cutting pattern is realized by using two cut-phases.

IN this paper, we consider a two-level optimization problem (S) (weak Stackelberg problem) in which the constraints of the upper level problem depend on the set of optimal solutions of the lower level problem, supposed not necessarily a singleton. Using penalty methods, we give an approximation...

In an exchange economy with no aggregate uncertainty, and Bayesian agents, Pareto optimal allocations provide full insurance if and only if the agents have a common prior. It is hard to explain why there is relatively so little betting taking place. One is led to ask, when are full insurance...