# 2015 Informs Annual Meeting

SA15

INFORMS Philadelphia – 2015

SA15 15-Franklin 5, Marriott Nonlinear Optimization in Energy Systems Sponsor: Optimization/Nonlinear Programming Sponsored Session Chair: Nai-Yuan Chiang, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL, United States of America, nychiang@mcs.anl.gov Co-chair: Yankai Cao,Ph.d. Student, Purdue University, FRNY G053B, 480 Stadium Mall Drive, West Lafayette IN 47907, United States of America, cao142@purdue.edu 1 - Clustering-Based Interior-Point Strategies for Convex Stochastic Programs Yankai Cao, PhD Student, Purdue University, FRNY G053B, 480 Stadium Mall Drive, West Lafayette, IN, 47907, United States of America, cao142@purdue.edu, Victor M. Zavala, Carl Laird We present a clustering-based interior-point strategy for two-stage stochastic programs. The key idea is to perform adaptive clustering of scenarios inside the solver. The resulting compressed KKT system is much smaller and is used as a preconditioner. We derive spectral and error properties for the preconditioner. We also describe our parallel implementation and demonstrate that high compression rates of 87% and speedups of 30 are achievable for electricity market clearing problems. 2 - Arc Search Methods for Linearly Constrained Optimization Nick Henderson, Research Associate and Instructor, Stanford University, Stanford, CA, nwh@stanford.edu We present an arc search algorithm for linearly constrained optimization. The method constructs and searches along smooth arcs that satisfy a small set of properties. When second derivatives are used, the method is shown to converge to a second-order critical point. We discuss use of arc search in Quasi-Newton methods and different strategies for handling constraints. 3 - A Progressive Method to Solve Large-scale AC Optimal Power Flow with Discrete Variables Maxime Fender, Optimization Consultant, Artelys Canada Inc., 2001 Boulevard Robert-Bourassa, #1700, Montréal, QC, H3A 2A6, Canada, maxime.fender@artelys.com, Manuel Ruiz, Jean Maeght, Alexandre Marié, Patrick Panciatici This study on power system networks aims to produce a dynamic simulation based security assessment taking into account uncertainties. An extended OPF without any guarantee on feasibility leads to the resolution of a Mixed-Integer NonLinear Problem, very challenging, and even harder to solve when the problem is not convex. A custom filtering method which tries to explain infeasibilities and uses the nonlinear solver KNITRO to reformulate discrete variables into nonlinear constraints is proposed. 4 - A Robust Approach to Chance Constrained Optimal Power Flow with Renewable Generation Yury Dvorkin, PhD Student/Research Assistant, University of Washington, 185 Stevens Way NE, Paul Allen Center, Room AE104R, Seattle, WA, 98195, United States of America, iouridvorkin@gmail.com, Miles Lubin, Scott Backhaus We formulate a Robust Chance Constrained (RCC) OPF that accounts for uncertainty in the parameters of these probability distributions by allowing them to be within an uncertainty set. The RCC OPF is solved using a scalable cutting- plane algorithm. We evaluate the RRC OPF on a modified BPA test system, which includes 2209 buses and 176 controllable generators. Deterministic, chance constrained (CC), and RCC OPF formulations are compared using several cost and reliability metrics. SA16 16-Franklin 6, Marriott Topics in Optimization Sponsor: Optimization/Linear and Conic Optimization Sponsored Session Chair: John Mitchell, Professor, Rensselaer Polytechnic Institute, Mathematical Sciences Dept, Troy, NY, 12180, United States of America, mitchj@rpi.edu 1 - A Rounding Procedure for a Maximally Complementary Solution of Semidefinite Optimization Problems Ali Mohammad Nezhad, PhD Student, Lehigh University, 200 West Packer Ave., Industrial and Systems Engineering Dept.,

In this paper, we deal with the identification of optimal partitioning in semidefinite optimization. We derive some bounds on the condition numbers of the problem using the first order theory of reals and estimate the magnitude of the eigenvalues in the vicinity of the central path, which depends on the degree of singularity of the optimality conditions. We then present a rounding procedure for the solution of an interior point method to get a maximally complementary solution. 2 - Convex and Structured Nonconvex Stochastic Optimization with Stochastic Constraints Zhiqiang Zhou, University of Florida, 2330 SW Williston RD, Apt3034, Gainesville, FL, 32608, United States of America, brianzhou1991@gmail.com, Guanghui Lan We present a new stochastic approximation (SA) algorithm to minimize a class of convex or nonconvex objective functions subject to certain expectation constraints. We show that this algorithm exhibits the optimal rates of convergence in expectation and with high probability under different conditions. Some numerical results are provided for portfolio management and machine learning. 3 - Benders Decomposition for Discrete-constrained Problems with Complementarity Constraints John Mitchell, Professor, Rensselaer Polytechnic Institute, Mathematical Sciences Dept, Troy, NY, 12180, United States of America, mitchj@rpi.edu, Jong-shi Pang, Andreas Waechter, Francisco Jara-Moroni We discuss a logical Benders decomposition approach to discrete-constrained mathematical programs with complementarity constraints. This is an extension of our prior approach to linear and quadratic programs with complementarity constraints. The inclusion of discrete and binary constraints broadens the applicability of the approach. SA17 17-Franklin 7, Marriott Social Network Modeling and Optimization Sponsor: Optimization/Network Optimization Sponsored Session Chair: Alexander Nikolaev, Assistant Professor, University at Buffalo (SUNY), 312 Bell Hall, Buffalo, NY, 14260-2050, United States of America, anikolae@buffalo.edu 1 - Seed Selection Scheduling for Long-term Campaign Planning on Large Social Networks Mohammadreza Samadi, PhD Candidate, University at Buffalo SUNY, 327 Bell Hall, Buffalo, NY, 14260, United States of America, msamadi@buffalo.edu, Alexander Nikolaev, Nagi Rakesh The influence maximization problem lies in finding a set of seeds that can optimally initiate a diffusion-driven cascade. We explore flexible, time-dependent seed activation solutions for long-term intervention/campaign planning on networks. The Seed Selection Scheduling Problem (SSSP) is that of selecting an optimal policy for seed activation over a finite time horizon under knapsack constraints. The ideas from the wireless sensor scheduling domain are used to tackle SSSP on large networks. 2 - Critical Nodes in Network Cohesion Alexander Veremyev, University of Florida, 1350 N Poquito Road, Shalimar, FL, United States of America, averemyev@ufl.edu, Oleg Prokopyev, Eduardo Pasiliao We consider a class of critical nodes detection problems that involves minimization of a graph cohesion measure (e.g., graph efficiency or harmonic average geodesic distance, Harary index, characteristic path length, communication utility) that depends on the actual pairwise distances between nodes in the remaining graph after nodes removal. We derive linear integer programming formulations along with additional enhancements, and develop an exact iterative algorithm to solve this problem. 3 - Detecting Cliques of Maximum and Minimum Centrality: Methods and Applications Chrysafis Vogiatzis, Assistant Professor, North Dakota State University, 1410 14th Avenue North, Room 202 Civil & Industrial Engineering, Fargo, ND, 58102, United States of America, chvogiat@ufl.edu, Alexander Veremyev In this talk, we consider the problem of finding the most and least “influential” or “influenceable” cliques in graphs based on three classical centrality measures: degree, closeness, and betweenness. In addition to standard betweenness, we also consider its optimistic and pessimistic counterparts along with a new metric for cluster closeness, namely residual closeness centrality. Applications discussed include analysis of information and social networks, and results on the stock market graph.

Bethlehem, PA, 18015, United States of America, ali.mohammadnezhad@gmail.com, Tamás Terlaky

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