2015 Informs Annual Meeting

TB16

INFORMS Philadelphia – 2015

TB15 15-Franklin 5, Marriott Recent Advances in Nonlinear Programming Sponsor: Optimization/Nonlinear Programming Sponsored Session Chair: Hande Benson, Associate Professor, Drexel University, LeBow College of Business, Philadelphia, PA, 19104, United States of America, hvb22@drexel.edu 1 - Solving the Problem of Portfolio VAR Minimization as a Nonlinear Program Arun Sen, Director, Navigant Consulting, 685 3rd Avenue, 14th Floor, New York, NY, 10017, United States of America, arunsen@alumni.princeton.edu Minimizing Value at Risk (VAR) is challenging as the optimization problem is non-convex. In previous work the problem was formulated as an MPEC (mathematical program with equilibrium constraints), that was solved using branch-and-bound techniques. We show that the same MPEC can be solved effectively as a nonlinear program, specifically by use of interior-point methods, and that this a flexible approach that is easily able to incorporate additional constraints on the optimal portfolio. 2 - Fast Algorithms for LAD Lasso Problems Robert Vanderbei, Princeton University, ORFE, Sherrerd Hall, Princeton, NJ, 08544, United States of America, rvdb@princeton.edu We will present a new algorithm for the LAD Lasso problem. We will compare this new algorithm against existing state-of-the-art algorithms. 3 - Cubic Regularization for First-order Methods Regularization techniques have been used to help existing algorithms solve “difficult” nonlinear optimization problems. Over the last decade, regularization has been proposed to remedy issues with equality constraints and equilibrium constraints, bound Lagrange multipliers, and identify infeasible problems. In this talk, we will focus on the application of cubic regularization in the context of the symmetric rank one and the conjugate gradient methods for nonlinear programming. 4 - Value Driven Design Delegation - An Optimization Model Vinod Cheriyan, Enova International, 1255 S Michigan Ave. Apt 3711, Chicago, IL, 60605, United States of America, vinod.cheriyan@gmail.com, Chris Paredis, Anton Kleywegt Rather than satisfaction of stakeholder needs, the Value Driven Design approach focuses on maximization of economic value. For large, complex systems, the systems designer maximizes the value by delegating detailed design to many subsystem teams. We study the convergence properties of such a value-driven, delegation-based system design process, where knowledge is distributed. We model the design as an optimization problem. We propose an algorithm and show that it converges to a critical point. TB16 16-Franklin 6, Marriott Various Aspects of Mixed Integer Conic Optimization Sponsor: Optimization/Linear and Conic Optimization Sponsored Session Chair: Sertalp Cay, Lehigh University, 200 W Packer Ave, Bethlehem, PA, 18015, United States of America, sec312@lehigh.edu 1 - Portfolio Optimization Problems with Cone Constraints and Discrete Decisions Umit Saglam, Assistant Professor, East Tennessee State University, Department of Management and Marketing, College of Business and Technology, Johnson City, TN, 37614, United States of America, saglam@etsu.edu, Hande Benson In this study we consider both single-period and multiperiod portfolio optimization problems based on the Markowitz (1952) mean/variance framework. Our model is aggregated from current literature.We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). We have devised and implemented the first solution method for such problems and demonstrate its efficiency on large-scale portfolio optimization models.We also provide substantial improvement in runtimes. David Shanno, RUTCOR - Rutgers University (Emeritus), Rutgers University, New Brunswick, NJ, United States of America, shannod@comcast.net, Hande Benson

2 - Optimal Averaging Schemes for Stochastic Approximation Methods

Farzad Yousefian, Postdoctoral Research Associate, Penn State, 333 Logan Ave., Apt. 307, State College, PA, 16801, United States of America, szy5@psu.edu, Angelia Nedich, Uday Shanbhag We develop optimal weighted averaging stochastic approximation schemes for solving stochastic variational inequality problems. We show that the gap function associated with the averaged sequence diminishes to zero at the optimal rate. We also develop a window-based variant of this scheme that displays the optimal rate and the superiority in the constant factor of the bound comparing to the classic averaging schemes. Preliminary numerical results on a stochastic Nash-Cournot game are presented. 3 - Adaptive Sampling Line Search for Local Simulation Optimization Raghu Pasupathy, Associate Professor, Department of Statistics, Purdue University, 250 N University Street, West Lafayette, IN, 47907, United States of America, pasupath@purdue.edu, Fatemeh Hashemi We present an algorithm for continuous simulation optimization that combines adaptive sampling ideas with a classical line search method from deterministic nonlinear programming. We will discuss theoretical properties and a brief example. 4 - Noisy Collective Nonconvex Optimization Mengdi Wang, Assistant Professor, Princeton University, 302 Trinity Ct #2, Princeton, NJ, 08540, United States of America, mengdiw@princeton.edu Paper not available at this time. TB14 14-Franklin 4, Marriott Joint Session OPT/ICS: Stochastic Programming: Progressive Hedging and Related Methods Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Jonathan Eckstein, Professor, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, United States of America, jeckstei@rci.rutgers.edu 1 - Scalable Lower and Upper Bounding Techniques for Stochastic Unit Commitment with Progressive Hedging Jean-paul Watson, Sandia National Laboratories, P.O. Box 5800, MS 1326, Albuquerque, United States of America, jwatson@sandia.gov, David Woodruff, Sarah Ryan We describe configurations of a scenario-based decomposition strategy for solving the stochastic unit commitment problem, based on the progressive hedging algorithm. We consider both upper and lower bounding aspects of progressive hedging in the mixed-integer case, and demonstrate parameterizations that yield extremely tight optimality gaps for 100-generator cases and moderately tight optimality gaps for 350-generator cases. 2 - Progressive Hedging and Dual Decomposition The PH algorithm proposed by Rockafellar and Wets and the DDSIP algorithm proposed by Caroe and Schultz can both be thought of as primal-dual algorithms and both can be used to address stochastic mixed-integer programs. In this talk I describe work with numerous co-authors to use the two algorithms together. In addition we describe an algebraic modeling language (Pyomo) interface to DDSIP that is useful with, or without, PH. 3 - Asynchronous Projective Progressive-hedging-like Stochastic Programming Decomposition Methods Jonathan Eckstein, Professor, Rutgers University, 100 Rockafeller Road, Piscataway, NJ, 08854, United States of America, jeckstei@rci.rutgers.edu We present a class of stochastic programming algorithms based on new Combettes-Eckstein monotone operator splitting methods. Unusually, these splitting methods need to re-solve only a subset of the subproblems at each iteration, using boundedly outdated information. Applying these techniques to stochastic programming yields methods that resemble progressive hedging, but can operate in a fully asynchronous manner. Convergence is guaranteed under the same conditions as for progressive hedging. David Woodruff, UC Davis, One Shields Avenue, Davis, CA, 95616, United States of America, dlwoodruff@ucdavis.edu

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