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 present a convex conic relaxation for a problem of maximising an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12/37 relative accuracy of the approximation. In the second part of the paper we derive the...

We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable.

We consider semidefinite programs, where all the matrices defining the problem commute. We show that in this case the semidefinite program can be solved through an ordinary linear program. As an application, we consider the max-cut problem, where the underlying graph arises from an association...

We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. The main contribution of this paper is a probably good convex quadratic programming relaxation of strongly polynomial size of this problem.

In facility layout problems, a major concern is the optimal design or remodeling of the facilities of an organization. The decision maker's objective is to arrange the facility in an optimal way, so that the interaction among functions (i.e. machines, inventories, persons) and places (i.e....

This paper studies models where the optimal response functions under consideration are non-increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be...

Programs that work very well in optimizing convex functions very often perform poorly when the problem has multiple local minima or maxima. They are often caught or trapped in the local minima/maxima. Several methods have been developed to escape from being caught in such local optima. The...

This paper adapts to the case of impulse and hybrid control systems the results obtained bu Aubin, Bicchi and Pancanti on "detectability" of solutions of usual control systems.

A generalization of the Roy-Gallai Theorem on the chromatic number of a graph is derived which is also an extension of several other results of Berge and of Li.