Consider the problem of minimizing, over a polyhedral set, the composition of an afline mapping with a strongly convex differentiable function. The polyhedral set is expressed as the intersection of an affine set with a (simpler) polyhedral set and a new local error bound for this problem, based on projecting the reduced gradient associated with the affine set onto the simpler polyhedral set, i...

Radzik (1991) showed that two-player games on compact intervals of the real line have ε – equilibria for all ε > 0, provided that payoff functions are upper semicontinuous and strongly quasi-concave. In an attempt to generalize this theorem, Ziad (1997) stated that the same is true for n-player games on compact, convex subsets of Rm, m ≥ 1 provided that we strengthen the upper semicontinuity co...

This paper discusses polyhedral approaches to problems in Domination Graph Thoery. We give various linear integer programming formulations for the weighted and unweighted versions of the minimum dominating set problem. We study the associated polytopes and determine dimension of the polytopes, facets, valid inequalities et al. Ideas from integer programming such as lift and project are used to ...

The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over polyhedron. Phase one of the algorithm nonmonotone gradient projection algorithm, while phase two an active set that explores faces constraint A gradient-based implementation presented, where projected version conjugate employed in two. Asymptotically, only performed. Comparisons are given with ...

Integration of heat and electricity supply improves the overall energy efficiency system operational flexibility. The renewable powered heat-electricity is a promising way to set up residential facilities in remote areas beyond reach power infrastructures. However, volatility wind solar brings about risk inadequacy. This article proposes data-driven robust method quantify two measures such stan...

A compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. Directed Hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. Sets of extrema of Birkhoff polyhedra are mapped to tours ...