相关论文: About the Complexity of Two-Stage Stochastic IPs

We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…

This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…

Bounded policy iteration is an approach to solving infinite-horizon POMDPs that represents policies as stochastic finite-state controllers and iteratively improves a controller by adjusting the parameters of each node using linear…

We prove the existence of an algorithm $A$ for computing 2-d or 3-d convex hulls that is optimal for every point set in the following sense: for every sequence $\sigma$ of $n$ points and for every algorithm $A'$ in a certain class…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

We develop and analyze stochastic variants of ISTA and a full backtracking FISTA algorithms [Beck and Teboulle, 2009, Scheinberg et al., 2014] for composite optimization without the assumption that stochastic gradient is an unbiased…

Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…

By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…

Recently the "SP" (Stochastic Polyak step size) method has emerged as a competitive adaptive method for setting the step sizes of SGD. SP can be interpreted as a method specialized to interpolated models, since it solves the interpolation…

We consider the utility maximization problem under convex constraints with regard to theoretical results which allow the formulation of algorithmic solvers which make use of deep learning techniques. In particular for the case of random…

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…

Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…

This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…

Given an undirected graph $G = (V,E)$ with a set of terminals $T\subseteq V$ partitioned into a family $\mathcal{S}$ of disjoint blocks, find the maximum number of vertex-disjoint paths whose endpoints belong to two distinct blocks while no…

The incremental gradient method is a prominent algorithm for minimizing a finite sum of smooth convex functions, used in many contexts including large-scale data processing applications and distributed optimization over networks. It is a…

We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We…

Stochastic gradient (SG) methods are fundamental to system identification and machine learning, enabling online parameter estimation in large-scale and streaming-data settings. As a classical identification method, the SG algorithm has been…

Benders decomposition is one of the most applied methods to solve two-stage stochastic problems (TSSP) with a large number of scenarios. The main idea behind the Benders decomposition is to solve a large problem by replacing the values of…

We propose a two-stage procedure for estimating the location $\bolds{\mu}$ and size M of the maximum of a smooth d-variate regression function f. In the first stage, a preliminary estimator of $\bolds{\mu}$ obtained from a standard…

Previous studies on two-timescale stochastic approximation (SA) mainly focused on bounding mean-squared errors under diminishing stepsize schemes. In this work, we investigate {\it constant} stpesize schemes through the lens of Markov…