-
作者：Sur, Arnab; Birge, John R.
作者单位：University of Chicago
摘要：In this article we study the consistency of optimal and stationary (KKT) points of a stochastic non-linear optimization problem involving expectation functionals, when the underlying probability distribution associated with the random variable is weakly approximated by a sequence of random probability measures. The optimization model includes constraints with expectation functionals those are not captured in direct application of the previous results on optimality conditions exist in the liter...
-
作者：Abdi, Ahmad; Cornuejols, Gerard; Huynh, Tony; Lee, Dabeen
作者单位：University of London; London School Economics & Political Science; Carnegie Mellon University; Monash University; Institute for Basic Science - Korea (IBS)
-
作者：Mueller, Benjamin; Munoz, Gonzalo; Gasse, Maxime; Gleixner, Ambros; Lodi, Andrea; Serrano, Felipe
作者单位：Zuse Institute Berlin; Universidad de O'Higgins; Universite de Montreal; Polytechnique Montreal
摘要：Themost important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In th...
-
作者：Shi, Bin; Du, Simon S.; Jordan, Michael, I; Su, Weijie J.
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; University of Washington; University of Washington Seattle; University of California System; University of California Berkeley; University of Pennsylvania
摘要：Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODES do not distinguish between two fundamentally different algorithms-Nesterov's accelerated gradient method for strongly convex functions (NAG-SC) and Polyak's heavy-ball method-we study an alternative limiting process that yields high-resolution ODEs. We show that these ODES permit a general Lyapunov function framework for the ana...
-
作者：Rujeerapaiboon, Napat; Schindler, Kilian; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
摘要：The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure of proximity between distributions, we identify those n-point distributions on the unit ball that are least susceptible to scenario re...
-
作者：Esteban-Perez, Adrian; Morales, Juan M.
作者单位：Universidad de Malaga
摘要：We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsi...
-
作者：Patel, Vivak
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Stopping criteria for Stochastic Gradient Descent (SGD) methods play important roles from enabling adaptive step size schemes to providing rigor for downstream analyses such as asymptotic inference. Unfortunately, current stopping criteria for SGD methods are often heuristics that rely on asymptotic normality results or convergence to stationary distributions, which may fail to exist for nonconvex functions and, thereby, limit the applicability of such stopping criteria. To address this issue,...
-
作者：Aliev, Iskander; Averkov, Gennadiy; De Loera, Jesus A.; Oertel, Timm
作者单位：Cardiff University; Brandenburg University of Technology Cottbus; University of California System; University of California Davis
摘要：We study the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries, which is referred to as the l(0)-norm of the vector. Our main results are new improved bounds on the minimal l(0)-norm of solutions to systems Ax = b, where A is an element of Z(mxn), b is an element of Z(m) and x is either a general integer vector (lattice case) or a non-negative integer vector (s...
-
作者：Salzo, Saverio; Villa, Silvia
作者单位：Istituto Italiano di Tecnologia - IIT; University of Genoa
摘要：We study the block-coordinate forward-backward algorithm in which the blocks are updated in a random and possibly parallel manner, according to arbitrary probabilities. The algorithm allows different stepsizes along the block-coordinates to fully exploit the smoothness properties of the objective function. In the convex case and in an infinite dimensional setting, we establish almost sure weak convergence of the iterates and the asymptotic rate o(1/n) for the mean of the function values. We de...
-
作者：Averkov, Gennadiy; Schymura, Matthias
作者单位：Brandenburg University of Technology Cottbus
摘要：For a set X of integer points in a polyhedron, the smallest number of facets of any polyhedron whose set of integer points coincides with X is called the relaxation complexity rc(X). This parameter, introduced by Kaibel & Weltge (2015), captures the complexity of linear descriptions of X without using auxiliary variables. Using tools from combinatorics, geometry of numbers, and quantifier elimination, we make progress on several open questions regarding rc(X) and its variant rcQ(X), restrictin...
