First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
In this paper, we study continuous time Markov decision processes (CTMDPs) with a denumerable state space, a Borel action space, unbounded transition rates and nonnegative reward function. The optimality criterion to be considered is the first passage risk probability criterion. To ensure the non-explosion of the state processes, we first introduce a so-called drift condition, which is weaker than the well known regular condition for semi-Markov decision processes (SMDPs). Furthermore, under some...
2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally...
In the paper a necessary condition is given for the existence of a minimal point of once continuously differentiable (generally non-convex) function over a general set.
The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in...
Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method for comparing decision making units (DMUs) with multiple inputs and multiple outputs. In conventional DEA, it is assumed that the status of each measure is clearly known as either input or output. However, in some situations, a performance measure can play input role for some DMUs and output role for others. Cook and Zhu [Eur. J. Oper. Res.180 (2007) 692–699] referred to these variables...
Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method for comparing decision making units (DMUs) with multiple inputs and multiple outputs. In conventional DEA, it is assumed that the status of each measure is clearly known as either input or output. However, in some situations, a performance measure can play input role for some DMUs and output role for others. Cook and Zhu [Eur. J. Oper. Res.180 (2007) 692–699] referred to these variables...
Nous modélisons ici plusieurs problèmes de Transport et de Gestion de Flux à l’aide d’un flot entier et d’un multiflot fractionnaire couplés par une contrainte de capacité. Pour le problème ainsi obtenu, nous proposons différents schémas de résolution par relaxation et décomposition, qui induisent la recherche d’un flot auxiliaire dont la partie entière supérieure doit minimiser un certain coût, et qui requièrent la mise en œuvre d’un processus d’agrégation. Nous en déduisons diverses heuristiques...
Nous modélisons ici plusieurs problèmes de Transport et de Gestion de Flux à l'aide d'un flot entier et d'un multiflot fractionnaire couplés par une contrainte de capacité. Pour le problème ainsi obtenu, nous proposons différents schémas de résolution par relaxation et décomposition, qui induisent la recherche d'un flot auxiliaire dont la partie entière supérieure doit minimiser un certain coût, et qui requièrent la mise en œuvre d'un processus d'agrégation. Nous en déduisons diverses heuristiques...
We derive new upper bounds for the densities of measurable sets in which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions . This gives new lower bounds for the measurable chromatic number in dimensions . We apply it to get a short proof of a variant of a recent result of Bukh which in turn generalizes theorems of Furstenberg,...
In this paper, we describe the methodology used to tackle France Telecom workforce scheduling problem (the subject of the Roadef Challenge 2007) and we report the results obtained on the different data sets provided for the competition. Since the problem at hand appears to be NP-hard and due to the high dimensions of the instance sets, we use a two-step heuristical approach. We first devise a problem-tailored heuristic that provides good feasible solutions and then we use a meta-heuristic scheme...