Informs 2015

291 / 552

INFORMS Philadelphia – 2015
289
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, , 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, ,
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,
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,
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,
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
David Woodruff, UC Davis, One Shields Avenue, Davis, CA,
95616, United States of America,
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,
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.
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,
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,
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,
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
David Shanno, RUTCOR - Rutgers University (Emeritus),
Rutgers University, New Brunswick, NJ, United States of
America, Hande Benson
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,
, 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,
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, , 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 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
also provide substantial improvement in runtimes.
TB16