Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which … Read more
We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems. Common to both strategies is their use of only the final (optimal) iterate of the initial problem and their negligible computational cost. This is a major advantage when comparing to … Read more
In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the … Read more
This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. … Read more
In this paper we present a variant of the conjugate gradient (CG) algorithm in which we invoke a subspace minimization subproblem on each iteration. We call this algorithm CGSO for “conjugate gradient with subspace optimization”. It is related to earlier work by Nemirovsky and Yudin. We apply the algorithm to solve unconstrained strictly convex problems. … Read more
In this paper, we propose a smoothing sequential quadratic programming (SSQP) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitz minimization problems, which has wide applications in statistics and sparse reconstruction. At each step, the SSQP algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple … Read more
We consider the facility location problem with submodular penalty (FLPSP) and the facility location problem with linear penalty (FLPLP), two extensions of the classical facility location problem (FLP). First, we introduce a general algorithmic framework for a class of covering problems with submodular penalty, extending the recent result of Geunes et al. [12] with linear … Read more
Modifying von Neumann’s alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space. CitationNonlinear Analysis Series A: Theory, Methods & Applications, … Read more
This paper is mainly devoted to the study and applications of H\”older metric subregularity (or metric $q$-subregularity of order $q\in(0,1]$) for general set-valued mappings between infinite-dimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and pointbased sufficient conditions as well as necessary conditions for $q$-metric subregularity with evaluating the exact … Read more
We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. CitationTo appear in: Computational and Analytical Mathematics. Springer Proceedings in MathematicsArticleDownload View PDF