We propose a novel, ecient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). Our approach combines a greedy hillclimbing algorithm and a cyclic permutation method. When searching for optimal ER-fMRI designs, the proposed approach focuses only on a promising restricted class of designs with equal frequency of occurrence across stimulus … Read more
In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian … Read more
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
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