In this work, we study the \emph{orientation model} for vertex coloring problems with the aim of finding partial descriptions of the associated polytopes. We present new families of valid inequalities, most of them supported by paths of the input graph. We develop facet-generating procedures for the associated polytopes, which we denominate \emph{path-lifting procedures}. Given a … Read more
Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal on Optimization 18, pp. 1286-1309, 2008]. Complexity results that report its worst-case behavior in terms of iterations and evaluations of functions and … Read more
This paper presents a tutorial on the state-of-the-art methodologies for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. The methodologies are classifi ed according to the decomposition alternatives and the types of the variables in the problem. We review the fundamentals of Benders Decomposition, Dual Decomposition … Read more