2016 INFORMS Annual Meeting Program

WE13

INFORMS Nashville – 2016

2 - Optimization Of Large Scale Tennessee Bioenergy Production From Field To Blending Facility Lixia He-Lambert, University of Tennessee, 2621 Morgan Circle, 310 Morgan Hall, Knoxville, TN, 37996, United States, llamber3@utk.edu, Burton C. English, James Larson, Tun-Hsiang Edward Yu, Bradly Wilson, Oleg Shylo A large scale spatial-oriented mixed integer linear model was developed to maximize the net present value of the Tennessee switchgrass-based biofuel supply chain. Location of the production of feedstock within each five square-mile hexagon was determined along with the location of candidate preprocessing centers and biorefinaries. Shipping routes from field, and from biorefinary to biorefinary and to blending facilities were determined. WE11 104A-MCC Sequential Stochastic Optimization Sponsored: Optimization, Optimization Under Uncertainty Sponsored Session Chair: Xiangyu Gao, University of Illinois, 04 Transportation Building, 104 S. Mathews Ave, Urbana, IL, 61801, United States, xgao12@illinois.edu 1 - A Transformation Technique For Stochastic Optimization With A common technical issue encountered in many operations management models is that decision variables are truncated by some random variables. The challenge arising from this problem is that the objective functions are not convex in the decision variables due to the truncation. To address this challenge, we develop a powerful transformation technique which converts a non-convex minimization problem to an equivalent convex minimization problem. We show that such a transformation enables us to prove the preservation of some desired structural properties,such as convexity, submodularity and L^natural-convexity, under optimization operations. 2 - Stochastic Optimal Control Based Rental Of Production Capacity Under Uncertain Production Requirements Maurizio Tomasella, University of Edinburgh, Edinburgh, United Kingdom, Maurizio.Tomasella@ed.ac.uk, Artur Korinski We model and analyse problems related to the optimal rental of manufacturing capacity, when requirements for both demand and product technical specifications evolve stochastically over time. We study a number of variants of business models of capacity rental. Adopting Stochastic Optimal Control based formulations, we derive the optimal closed-form policies that lead to choosing rental solutions with respect to the more established models of full ownership of manufacturing technology. A numerical case example involving high power fiber laser sources, one of the leading technologies in materials processing, shows the applicability of our optimal policies to real production environments. WE12 104B-MCC Recent Advances in Optimization and Related Topics Sponsored: Optimization, Integer and Discrete Optimization Sponsored Session Chair: Sebastian Pokutta, Georgia Institute of Technology, Ferst Dr., Atlanta, GA, 30308, United States, sebastian.pokutta@isye.gatech.edu 1 - Structured Learning Revisited Daniel Zink, Georgia Institute of Technology, Atlanta, GA, United States, daniel.zink@gatech.edu, Sebastian Pokutta, Gabor Braun Frank-Wolfe techniques are popular due to their simplicity and more recently Frank-Wolfe algorithms also gained significant traction for online learning. We propose a new algorithm in the setting of online combinatorial optimization, where the underlying feasible region is a 0/1 polytope P (e.g., paths in a graph). We achieve the same regret bounds and convergence rates as Frank-Wolfe techniques both in the online case and offline case, while gaining a significant speed up in computation time. Moreover, our bounds hold in the online structured learning setting, only depending on the l1-diameter of P and independent of its actual (very large) dimension d. Decisions Truncated By Random Variables Xiangyu Gao, UIUC, Urbana, IL, United States, xgao12@illinois.edu, Xin Chen, Zhan Pang

2 - Approximate Hierarchical Clustering Via Lps Aurko Roy, Georgia Institute of Technology, Atlanta, GA, United States, aurko@gatech.edu, Sebastian Pokutta We study a cost function for hierarchical clusterings introduced by a recent work of Dasgupta for which a top-down algorithm was given that returns a hierarchical clustering of cost at most O(log1.5 n) times the optimal cost, using the ARV sparsest cut algorithm as a subroutine. We improve this by giving an O(log n)- approximation algorithm for this problem. Our main technical ingredients are a combinatorial characterization of ultrametrics induced by this cost function, deriving an IP formulation for this family of ultrametrics, and showing how to round an LP relaxation of this formulation by using the idea of sphere growing which has been extensively used in the context of graph partitioning. 3 - On The Computational Complexity Of Optimizing Over The Chvatal Closure Of A Polytope Dabeen Lee, PhD Student, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, United States, dabeenl@andrew.cmu.edu, Gerard P Cornuejols, Yanjun Li In this paper, we study the computational complexity of some problems that arise when taking the Chvatal closure of a polyhedron. Given a rational polytope contained in the unit hypercube or a rational simplex that does not contain any integer point, we prove that deciding emptiness of its Chvatal closure is NP- complete. It has two implications; first, it is NP-hard to check whether a given rational polytope contained in the unit hypercube or a rational simplex has Chvatal rank 1; second, the optimization and separation problem over the Chvatal closure of a given rational polytope contained in the unit hypercube or a rational simplex is NP-hard as well. WE13 104C-MCC Disciplined Convex Programming for Nonconvex Problems Sponsored: Optimization, Computational Optimization and Software Sponsored Session Chair: Miles Lubin, Massachusetts Institute of Technology-ORC, MIT, Cambridge, MA, 00000, United States, mlubin@mit.edu 1 - Polyhedral Approximation In Mixed-integer Convex Optimization Miles Lubin, Massachusetts Institute of Technology, Cambridge, MA, United States, mlubin@mit.edu, Emre Yamangil, Juan Pablo Vielma, Russell Bent We present recent developments in the polyhedral outer approximation algorithm for mixed-integer convex optimization derived from using disciplined convex programming to automatically generate extended formulations from a user’s algebraic input. 2 - Disciplined Convex-concave Programming Steven Diamond, Stanford University, Stanford, CA, United States, diamond@cs.stanford.edu, Xinyue Shen, Yuantao Gu, Stephen P Boyd In this talk we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP). Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a sum of a convex and a concave term. By combining CCP with DCP, we obtain an automated system for applying CCP that correctly handles subtleties such as the domains of functions and nondifferentiability on the boundary of domains. We describe a Python implementation called DCCP, which extends CVXPY. 3 - Outer-approximation Techniques For Mixed-integer Semidefinite Optimization Christopher Coey, Doctoral Student, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States, coey@mit.edu, Miles Lubin, Emre Yamangil, Juan Pablo Vielma, Russell Bent We will present an extension of the outer-approximation algorithm in Pajarito for mixed-integer semidefinite optimization problems, and test the new approach with computational experiments.

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