We consider the problem of maximizing influence in a social network. We focus on the case that the social network is a directed bipartite graph whose arcs join senders to receivers. We consider both the case of deterministic networks and probabilistic graphical models, that is, the so-called “cascade” model. The problem is to find the … Read more
The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems including those of conic and specifically semidefinite programming. Developing a new technique of variational analysis and generalized differentiation, we derive second-order characterizations of full stability, in both Lipschitzian and H\”olderian … Read more
We investigate the computational potential of split inequalities for non-convex quadratic integer programming, first introduced by Letchford and further examined by Burer and Letchford. These inequalities can be separated by solving convex quadratic integer minimization problems. For small instances with box-constraints, we show that the resulting dual bounds are very tight; they can close a … Read more
We developed a modular framework to obtain exact and approximate solutions to a class of linear optimization problems with recourse with the goal to minimize the worst-case expected objective over an ambiguity set of distributions. The ambiguity set is specified by linear and conic quadratic representable expectation constraints and the support set is also linear … Read more
The paper presents complete characterizations of Lipschitzian full stability of locally optimal solutions to problems of second-order cone programming (SOCP) expressed entirely in terms of their initial data. These characterizations are obtained via appropriate versions of the quadratic growth and strong second-order sucient conditions under the corresponding constraint quali cations. We also establish close relationships between … Read more
The trust region subproblem concerns the minimization of a general quadratic over the unit ball in R^n. Extensions to this problem are of interest because of applications to, for example, combinatorial optimization. However the extension obtained by adding an arbitrary family of linear side constraints is NP-hard. In this paper we consider variants of the … Read more
In this paper we propose an inexact proximal point method to solve constrained minimization problems with locally Lipschitz quasiconvex objective functions. Assuming that the function is also bounded from below, lower semicontinuous and using proximal distances, we show that the sequence generated for the method converges to a stationary point of the problem. CitationJuly 2013ArticleDownload … Read more
We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides … Read more
We consider a model in which a consumer of a resource over several periods must pay a per unit charge for the resource as well as a peak charge. The consumer has the ability to reduce his consumption in any period at some given cost, subject to a constraint on the total amount of reduction … Read more
We propose a polynomial algorithm for linear programming. The algorithm represents a linear optimization or decision problem in the form of a system of linear equations and non-negativity constraints. Then it uses a procedure that either fi nds a solution for the respective homogeneous system or provides the information based on which the algorithm rescales the … Read more