2016 INFORMS Annual Meeting Program

MB17

INFORMS Nashville – 2016

2 - Decentralized Primal-dual Gradient Method Soomin Lee, Georgia Institute of Technology, Atlanta, GA, United States, soomin.lee@isye.gatech.edu We present a decentralized primal-dual gradient method for optimizing a class of finite-sum convex optimization problem whose objective function is given by the summation of m smooth components together with other relatively simple terms. The smooth components are distributed over a network of m agents with time- varying topology, but all agents share common components whose structure is suitable for efficiently computing the proximal operator. In our method, each agent alternatively updates its primal and dual estimates by computing the primal and dual proximal operator, and by communicating these estimates with other agents in the network. We provide convergence results of this method. 3 - Decomposing Linearly Constrained Nonconvex Problems By A Proximal Primal Dual Approach Mangyi Hong, Iowa State University, mingyi@iastate.edu We propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. We show that whenever the penalty parameter in the augmented Lagrangian is larger than a given threshold, the Prox-PDA converges to the set of stationary solutions, globally and in a sublinear manner. Interestingly, when applying a variant of the Prox-PDA to the problem of distributed nonconvex optimization (over a connected undirected graph), the resulting algorithm coincides with the popular EXTRA algorithm, which is only known to work in convex cases. MB16 105A-MCC Data-driven and Robust Optimization Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Linwei Xin, U of Illinois at Urbana-Champaign, Urbana, IL, 61801, United States, lxin@illinois.edu 1 - Distributionally Robust Stochastic Optimization With Wasserstein Distance Rui Gao, Georgia Institute of Technology, rgao32@gatech.edu, Anton J Kleywegt We consider a distributionally robust stochastic optimization (DRSO) problem, in which the ambiguity set contains all the distributions that are close to the nominal distribution in terms of Wasserstein distance and satisfies certain correlation structure. Comparing to the widely-used -divergence and moment method, Wasserstein distance yields a more reasonable worst-case distribution. We derive a tractable dual reformulation of the DRSO by constructing the worst- case distribution explicitly via the first-order optimality condition. 2 - Robust Extreme Event Analysis Clementine Mottet, Boston University, cmottet@bu.edu, Henry Lam We propose a robust optimization approach to estimate extreme event performance measures. This approach aims to alleviate the issue of model misspecification encountered by conventional statistical methods that is amplified by a lack of data typically occurring in the tail region. We demonstrate the use of shape constraints to mitigate this issue and develop a solution scheme for the resulting optimizations. We show some numerical results and compare our approach to extreme value theory. 3 - Data-driven Optimization Of Reward-risk Ratio Measures Ran Ji, George Mason University, Fairfax, VA, 22030, United States, jiran@gwu.edu, Miguel Lejeune We study a class of distributionally robust optimization problems with ambiguous expectation constraints on reward-risk ratios. We develop a reformulation and algorithmic framework based on the Wasserstein metric to model ambiguity and to derive probabilistic guarantees that the ambiguity set contains the true probability distribution. The reformulation phase involves the derivation of the support function of the ambiguity set and the concave conjugate of the ratio function. We design bisection algorithms to efficiently solve the reformulation. We specify new ambiguous portfolio optimization models for various ratios. Computational results will be presented.

4 - Two-stage Distributionally Robust Unit Commitment Using Moment Information Yuanyuan Guo, University of Michigan, yuanyg@umich.edu Ruiwei Jiang As the renewable energy takes a growing share of the electricity markets, a considerable number of new renewable generators (e.g., wind and solar farms) are incorporated into daily power system operations. Because of fluctuating weather conditions or a lack of complete historical data, it can be challenging to accurately estimate the joint probability distribution of the renewable energy. In this paper, based on a small amount of historical data, we propose a two-stage distributionally robust unit commitment model that considers a set of plausible probability distributions. This model is less conservative than classical robust unit commitment models. MB17 105B-MCC Risk Measures on Stochastic Programs Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Saravanan Venkatachalam, Wayne State University, 42 W. Warren Ave, Detroit, MI, 48202, United States, saravanan.v@wayne.edu 1 - A Computational Study Of Recent Approaches To Risk-averse Stochastic Optimization Alexander Vinel, Auburn University, 3301 Shelby Center, Auburn, AL, 36849, United States, alexander.vinel@auburn.edu We present a computational study evaluating some recent approaches to risk- averse stochastic optimization. We focus on the classes of coherent and convex measures of risk, including higher-moment coherent measures and certainty- equivalent convex measures. While the bigger part of the study is devoted to portfolio optimization model, other problems with real-life data are considered. Our main goal is to evaluate the performance of various recently proposed techniques and determine the properties that can be used in guiding the specific choices of decision criteria in practice. 2 - Risk Parity In The Context Of Risk-averse Stochastic Optimization Nasrin Mohabbati Kalejahi, PhD Student, Auburn University, Auburn, AL, United States, nasrin@auburn.edu, Alexander Vinel The concept of risk parity has been recently studied in the area of financial portfolio management. The idea behind it is to promote diversification in the portfolio by ensuring that each asset is equally contributing to the total risk. In this work we propose to consider risk parity in the context of modern risk measure theory, by studying risk parity based on conditional value-at-risk and other coherent measures. We are interested in evaluating the quality of the decisions that arise from this stochastic optimization framework in both financial and engineering applications. 3 - Computational Study For Two-stage Stochastic 0-1 Integer We present a methodology for absolute semi-deviation (ASD) risk-measure for stochastic 0-1 programs. ASD risk-measure models lack the typical block structure amenable for decomposition. The proposed methodology uses information from expected excess, and uses cutting planes based on sub-gradient information. Computational results for a supply chain application will be presented. 4 - Decomposition For Multistage Stochastic Programs With Quantile And Deviation Risk Measures Prasad Parab, PhD Student, Texas A&M University, College Station, TX, United States, prasaddparab@tamu.edu, Lewis Ntaimo We present decomposition for multistage stochastic linear programs (MSLPs) with quantile and deviation mean-risk measures. Incorporating certain risk measures makes MSLPs very difficult to decompose and solve. In particular, we study stochastic decomposition based algorithms for MSLPs with quantile deviation and absolute semideviation risk measures. A comparative study of the two mean-risk measures will be presented. Programs With Absolute Semi Deviation Risk Measure Saravanan Venkatachalam, Wayne State University, Saravanan.v@wayne.edu, Lewis Ntaimo

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