In this paper we examine the impact of using the Sherali-Adams procedure on highly symmetric integer programming problems. Linear relaxations of the extended formulations generated by Sherali-Adams can be very large, containing on the order of n choose d many variables for the level-d closure. When large amounts of symmetry are present in the problem … Read more
This article investigates extremality, stationarity, and regularity properties of infinite collections of sets in Banach spaces. Our approach strongly relies on the machinery developed for finite collections. When dealing with an infinite collection of sets, we examine the behaviour of its finite subcollections. This allows us to establish certain primal-dual relationships between the stationarity/regularity properties … Read more
In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects — slopes — are introduced and a classification scheme of error bound criteria is presented. CitationPublished in Vietnam Journal … Read more
This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger & L�pez (2012) and is mainly focused on the application of the criteria from Kruger & L�pez (2012) to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly … Read more
We present an extension of the proximal point method with Bregman distances to solve Variational Inequality Problems (VIP) on Hadamard manifolds (simply connected finite dimensional Riemannian manifold with nonpositive sectional curvature). Under some natural assumption, as for example, the existence of solutions of the (VIP) and the monotonicity of the multivalued vector field, we prove … Read more
Several modifications of the limited-memory variable metric BNS method for large scale unconstrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used di®erence vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all … Read more
We propose a new first-order splitting algorithm for solving jointly the primal and dual formulations of large-scale convex minimization problems involving the sum of a smooth function with Lipschitzian gradient, a nonsmooth proximable function, and linear composite functions. This is a full splitting approach in the sense that the gradient and the linear operators involved … Read more
This paper introduces novel numerical solution strategies for generalized semi-infinite optimization problems (GSIP), a class of mathematical optimization problems which occur naturally in the context of design centering problems, robust optimization problems, and many fields of engineering science. GSIPs can be regarded as bilevel optimization problems, where a parametric lower-level maximization problem has to be … Read more
This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we … Read more
This article addresses a general criterion providing a zero duality gap for convex programs in the setting of the real locally convex spaces. The main theorem of our work is formulated only in terms of the constraints of the program, hence it holds true for any objective function fulfilling a very general qualification condition, implied … Read more