# 2015 Informs Annual Meeting

SA14

INFORMS Philadelphia – 2015

3 - Approximation Tools for Structured Nonconvex Optimization Problems

We propose a novel inferential framework for estimating large-scale spatial graphical models with a total cardinality constraint. This work has two major contributions. (i) From a computational perspective, we show that the computational accuracy increases when the problem scale increases. (ii) From a statistical perspective, we justify the obtained graph estimator achieves the minimax optimal rate of convergence under weak assumptions. 2 - A General Theory of Pathwise Coordinate Optimization Tuo Zhao, Johns Hopkins University, 12124 East Run Drive, Lawrenceville, NJ, 08648, United States of America, tourzhao@gmail.com, Tong Zhang, Han Liu The pathwise coordinate optimization achieves superior empirical performance for solving high dimensional nonconvex sparse learning problems, but at the same time poses significant challenge to theoretical analysis. To tackle this long lasting problem, we develop a new theory showing that the unique algorithmic structure of the pathwise coordinate optimization plays pivotal roles in guaranteeing its optimal statistical and computational performance. SA14 14-Franklin 4, Marriott Stochastic Optimization with Discrete Moments Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Anh Ninh, College of William and Mary, 200 Stadium Dr, Williamsburg, VA, 23186, United States of America, ninhtuananh@gmail.com 1 - Binomial Moments and Boolean Bounding for Functions in Random Variables Jinwook Lee, Drexel University, 3220 Market Street, Philadelphia, PA, United States of America, jw78kr@gmail.com, Jongpil Kim, Andras Prekopa For a desirable statistical precision level, it is often required to run a simulation more than million times. A new mathematical model is introduced for sharp bounds of a function of random variables. For the model construction we use the binomial moment scheme for systematic mathematical representation, and it’s further developed by the use of Boolean logic over set algebra. Numerical examples of various probability distributions are presented. 2 - Improved Bounds on the Probability of the Union of Events Some 100 Rockafeller Rd, Piscataway NJ 08854, United States of America,kunikazu.yoda@rutgers.edu, Andras Prekopa We formulate a linear program whose optimal objective function value can be used in other formulations to yield improved upper and lower bounds on the probability of the union of events if we know some empty intersections of small numbers of events. The LP relaxation of an extension of the maximum independent set problem provides an upper bound on the largest number of events that have a nonempty intersection. We present numerical experiments demonstrating the effectiveness of our formulation. 3 - New Methods for Probabilistically Constrained Optimization Problem with Degenerate Distribution Olga Myndyuk, Rutgers University, 100 Rockafeller Rd, Piscataway, NJ, 08854, United States of America, olik.myn@gmail.com The problem under consideration is probabilistically constrained optimization problem with degenerate continuous probability distribution of the random variables in the constraints.Upper and lower bounds were obtained using the results of A.Prekopa and degeneracy of the distributions. Existing and new methods for solving are discussed:supporting hyperplane method, Prekopa- Vizvari-Badics hybrid algorithm and two derivative-free methods. 4 - Some Aspects of Discrete Moment Problem from the Linear Programming Perspective: Numerical Approach Mariya Naumova, Rutgers University, Dept. of Mathematics, 110 Frelinghuysen Rd., Piscataway, NJ, 08854, United States of America, mariya.v.naumova@gmail.com We present a brief survey of some of the basic results related to the discrete moment problems. We illustrate how piecewise polynomial lower and upper bounds on the function, created in connection with suitable dual feasible bases in the univariate discrete moment problem can be used to approximate definite integrals. Numerical illustrations of valuations of financial instruments are presented. of Whose Intersections are Empty Kunikazu Yoda, Rutgers University,

Fatma Kilinc Karzan, Assistant Professor Of Operations Research, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, United States of America, fkilinc@andrew.cmu.edu, Levent Tuncel We study the structured nonconvex optimization problem of maximizing a convex function over a convex domain. Such problems generalize computing matrix norms and often arise in applications in robust optimization and machine learning. In many cases, these problems are NP-Hard; and thus we establish a framework for building tractable convex relaxations. We study various properties, approximation quality, and exactness of these relaxations, and establish connections to existing results. Surrogate-Based and Derivative-Free Optimization I Sponsor: Optimization/Mixed Integer Nonlinear Optimization and Global Optimization Sponsored Session Chair: Rommel Regis, Saint Joseph’s University, Mathematics Department, 5600 City Avenue, Philadelphia, 19131, United States of America, rregis@sju.edu 1 - A Swarm Intelligence Based Data-driven Optimizer using Adaptive Meta-modeling Mengqi Hu, University of Illinois at Chicago, Chicao, IL, United States of America, mhu@uic.edu Although many different meta-models are developed to reduce computational cost for time-intensive model, it is not conclusive that any meta-model performs better than others across diverse set of problems. To this end, we develop an adaptive model selection algorithm to adaptively select the most suited meta- model for different problems. This approach is integrated with a novel swarm intelligence algorithm for data-driven optimization which can achieve good result with less computational cost. 2 - Response Correction Techniques for Multifidelity Design Optimization Leifur Leifsson, Iowa State University, Department of Aerospace Simulations are widely used in engineering for analysis and design. A key challenge is the computational cost. Conventional design techniques typically require a large number of model evaluations. Thus, the use of simulations in the design process can be prohibitive. Physics-based surrogates, so-called multifidelity models, can be used to accelerate the optimization process. This talk describes several response correction techniques developed specifically for multifidelity design optimization. 3 - FALCON: A Function Approximation Algorithm for Large-scale Constrained Black-box Optimization Engineering, 2271 Howe Hall, Ames, IA, 50011, United States of America, leifur@iastate.edu SA12 12-Franklin 2, Marriott

Rommel Regis, Saint Joseph’s University, Mathematics Department, 5600 City Avenue, Philadelphia, PA, 19131, United States of America, rregis@sju.edu

This talk presents the FALCON algorithm for constrained expensive black-box optimization that uses surrogates to approximate the objective and constraint functions. Unlike previous methods, FALCON can handle infeasible start points and equality constraints. FALCON is implemented using an interpolating radial basis function surrogate and compared with alternatives on benchmark problems, including a large-scale automotive application with 124 decision variables and 68 black-box constraints.

SA13 13-Franklin 3, Marriott Nonconvex Statistical Optimization Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session

Chair: Han Liu, Princeton University, Sherrerd Hall, Charlton Street, Princeton, NJ, United States of America, hanliu@princeton.edu 1 - Blessing of Massive Scale: Spatial Graphical Model Inference with a Total Cardinality Constraint Ethan X. Fang, Princeton University, Sherrerd Hall ORFE, Charlton Street, Princeton, NJ, 08544, United States of America, ethanfangxy@gmail.com, Han Liu, Mengdi Wang

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