We shape a formal framework for distinguishing the behaviour of constructive and non-constructive polynomial time approximation algorithms for NP optimization problems. We introduce a new class, called SubNPO, that includes NPO and also some other problems used in recent works.

We draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new types of results...

We consider a financial market consisting of a nonrisky asset and a risky one. We study the minimal initial capital needed in order to super-replicate a given contingent claim under the Gamma constraint, i.e. a constraint on the unbounded variation part of the hedging porfolio. In the general...

In a first time we draw a rough shape of a general formal framework for polynomial approximation theory which encompasses the existing one by allowing the expression of new types of results. We show how this framework incorporates all the existing approximation results and, moreover, how new...

We establish necessary conditions of optimality for problems of optimal control Theory in the discrete time framework with infinite horizon. Our necessary conditions are in the form of Pontryagin principles. We treat smooth and partially nonsmooth settings, without concavity. A strong motivation...

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...

L'origine de ce travaial reside dans la question, dite teleologique, de la justification de scenarios determines par optimisation intertemporelle, pour les modeles macroeconomiques d'une economie non planifiee, mais susceptible de regulation. On aborde cette question par un approche constructive...

In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of Backward SDE's and forward-backward SDE's. The controlled process takes values in RXR and a given initial data for X(O). Then, the control problem is to find the...

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.