In this paper the issue of mathematical programming and optimization has being revisited. The theory of optimization deals with the development of models and methods that determine optimal solutions to mathematical problems defined. Mathematical model must be some function of any solution that...

Tucker's well-known combinatorial lemma states that for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {1,2,...n,-1,-2,....-n} with the property that antipodal vertices on the...

Tucker's well-known combinatorial lemma states that for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {+/-1,+/-2,...,+/-n} with the property that antipodal vertices on the...

Assortment optimization is an important problem in revenue management arising in industries such as online advertising, retailing and airline ticketing. We study assortment optimization under an arbitrary mixture of multi-nomial logit (MNL) models, when the universe of products is dense. In...

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the...

In this paper, we state sufficiency, necessity, convergence, existence and uniqueness results for infinite horizon optimal control problems with unbounded payoffs in which the assumptions are very weak and there are no topological assumptions about the model components. We also state a sequence...

Investors typically measure an asset’s potential to diversify a portfolio by its correlations with the portfolio’s other assets, but correlation is useful only if it provides a good estimate of how an asset’s returns co-occur cumulatively with the other asset returns over the investor’s...

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in the problem's parameters. The classical robust counterpart (RC) of the problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set, and...

We consider the solution of a recurrent sub–problem within both constrained and unconstrained Nonlinear Programming: namely the minimization of a quadratic function subject to linear constraints. This problem appears in a number of LBM frameworks, and to some extent it reveals a close analogy...

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters...