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作者：Pantuso, Giovanni; Hewitt, Mike
作者单位：University of Copenhagen; Loyola University Chicago
摘要：In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and feasibility cuts for both linear and integer stochastic programs. Extensive tests on three production planning problems illustrate that the method is extremely effective on large-scale instances.
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作者：Shen, Han; Xiao, Quan; Chen, Tianyi
作者单位：Rensselaer Polytechnic Institute
摘要：Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement learning. However, bilevel optimization problems are traditionally known to be difficult to solve. Recent progress on bilevel algorithms mainly focuses on bilevel optimization problems through the lens of the implicit-gradient method, where the lower-level objective...
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作者：De Loera, Jesus A.; Marsters, Brittney; Xu, Luze; Zhang, Shixuan
作者单位：University of California System; University of California Davis; Texas A&M University System; Texas A&M University College Station
摘要：We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a notion of finite generating set with the help of a group action. We show this is true for the cone of positive semidefinite matrices (PSD) and the second-order cone (SOC). Both cones have a finite generating set of integer points, similar in spirit to Hilbe...
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作者：Cartis, Coralia; Zhu, Wenqi
作者单位：University of Oxford
摘要：High-order tensor methods for solving both convex and nonconvex optimization problems have recently generated significant research interest, due in part to the natural way in which higher derivatives can be incorporated into adaptive regularization frameworks, leading to algorithms with optimal global rates of convergence and local rates that are faster than Newton's method. On each iteration, to find the next solution approximation, these methods require the unconstrained local minimization o...
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作者：Grimmer, Benjamin; Shu, Kevin; Wang, Alex L.
作者单位：Johns Hopkins University; California Institute of Technology; Purdue University System; Purdue University
摘要：The study of convex optimization has historically been concerned with worst-case convergence rates. The development of the Optimized Gradient Method (OGM), due to Drori and Teboulle [1] and Kim and Fessler [2], marked a major milestone in this study, as OGM achieves the optimal worst-case convergence rate among all first-order methods for unconstrained smooth convex optimization. In order to examine the possibility of obtaining stronger convergence guarantees, we will consider algorithms with ...
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作者：Chervet, Patrick; Grappe, Roland; Vallee, Mathieu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I); Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Information Sciences & Technologies (INS2I)
摘要：Totally equimodular matrices generalize totally unimodular matrices and arise in the context of box-totally dual integral polyhedra. This work further explores the parallels between these two classes and introduces foundational building blocks for constructing totally equimodular matrices. Consequently, we present a decomposition theorem for totally equimodular matrices of full row rank. Building on this decomposition theorem, we prove that simplicial cones whose generators form the rows of a ...
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作者：Zhang, Junyu
作者单位：National University of Singapore
摘要：We investigate stochastic Bregman proximal gradient (SBPG) methods for minimizing a finite-sum nonconvex function Psi(x):=1n & sum;i=1nfi(x)+phi(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi (x):=\frac{1}{n}\sum _{i=1}<^>nf_i(x)+\phi (x)$$\end{document}, where phi\documentclass[12pt]{minimal} \usepackage{a...
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作者：Bennouna, Amine; Van Parys, Bart P. G.
作者单位：Northwestern University; Massachusetts Institute of Technology (MIT); Centrum Wiskunde & Informatica (CWI)
摘要：We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish out-of-sample performance guarantees. Following (Van Parys et al. From data to decisions: Distributionally robust optimization is optimal. Management Science 2020) we take here the opposite approach. We define first a sensible yardstick with which to measure t...
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作者：Dussault, Jean-Pierre; Frappier, Mathieu; Gilbert, Jean Charles
作者单位：University of Sherbrooke; University of Sherbrooke
摘要：The semismooth Newton method is a very efficient approach for computing a zero of a large class of nonsmooth equations. When the initial iterate is sufficiently close to a regular zero and the function is strongly semismooth, the generated sequence converges quadratically to that zero, while the iteration only requires to solve a linear system. If the first iterate is far away from a zero, however, it is difficult to force its convergence using linesearch or trust regions because a semismooth ...
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作者：Huang, Kun; Pu, Shi; Nedic, Angelia
作者单位：The Chinese University of Hong Kong, Shenzhen; Arizona State University; Arizona State University-Tempe
摘要：In this paper, we introduce an accelerated distributed stochastic gradient method with momentum for solving the distributed optimization problem, where a group of n agents collaboratively minimize the average of the local objective functions over a connected network. The method, termed Distributed Stochastic Momentum Tracking (DSMT), is a single-loop algorithm that utilizes the momentum tracking technique as well as the Loopless Chebyshev Acceleration (LCA) method. We show that DSMT can asympt...
