2016 INFORMS Annual Meeting Program

SC15

INFORMS Nashville – 2016

SC13 104C-MCC” Advances in Mixed Integer Polynomial Optimization Sponsored: Optimization, Global Optimization Sponsored Session Chair: Akshay Gupte, Clemson University, O-321 Martin Hall, Clemson University, Clemson, SC, 29634, United States, agupte@clemson.edu 1 - Exploiting Permutation Invariance To Construct Tight Relaxations Mohit Tawarmalani, Purdue University, West Lafayette, IN, United States, mtawarma@purdue.edu, Jinhak Kim, Jean-Philippe P. Richard We construct the convex hull for a set that does not change when the variables are permuted. We illustrate the technique by developing (1) convex hull of matrices with bounded rank and spectral norms, (2) convex envelopes of multi- linear functions over certain domains, and (3) a novel reformulation and relaxation for sparse principal component analysis. 2 - Intersection Cuts And S-free Sets For Polynomial Optimization Chen Chen, Columbia University, New York, NY, United States, chen.chen@columbia.edu, Daniel Bienstock, Gonzalo Munoz We develop an intersection cut for generic problems with closed sets. The cut relies on a violation distance oracle and it can be computed in polynomial time in the special case of polynomial optimization. Additional cuts are presented based on S-free sets or convex forbidden zones; for polynomial optimization we adopt the specialized term of outer-product-free sets. We provide some insight into the nature of maximal outer-product-free sets and present two classes of such sets. These two classes give intersection cuts that can be computed in polynomial time. Furthermore, the associated intersection cuts can be strengthened in the case of intersections at infinity. 3 - On The Strength Of Linear Approximations For Multilinear Monomials We analyze worst-case errors associated with approximating multi-linear terms over bounded variables when using linear functions. The error associated with a linear function at a given point is the absolute difference between the actual and functional values. These errors turn out to be dependent on the variable bounds. We identify “best” linear functions that yield the smallest worst-case errors for various sets of bounds, and identify those points at which these errors are realized. The errors favorably compare with those obtained by convex hull representations. 4 - Iterative LP And SOCP-based Approximations To Semidefinite Programs Georgina Hall, Princeton University, Princeton, NJ, United States, gh4@princeton.edu, Amir Ali Ahmadi We develop techniques for approximating SDPs with LPs and SOCPs. Our algorithms iteratively grow an inner approximation to the PSD cone using a column generation scheme and/or a change of basis scheme involving Cholesky decompositions. Yibo Xu, Clemson University, Clemson, SC, United States, yibox@clemson.edu, Warren P Adams, Akshay Gupte

2 - Balancing Weather Risk And Crop Yield For Soybean Variety Selection Ling Tong, University of Iowa, Iowa City, IA, United States, ling-tong@uiowa.edu, Bhupesh Shetty, Samuel Burer We propose an optimization-based method to assist a farmer’s choice of soybean varieties to plant in order to maximize expected yield while also managing risk, where the primary uncertainty faced by the farmer is due to seasonal weather patterns. By solving a sequence of MIPs, we calculate the efficient frontier between the two competing objectives of maximizing expected yield and guaranteed yield over all possible season types. The coefficients of the MIPs are estimated using a multiple-linear-regression model and a Bayesian-updating scheme applied to the training and evaluation data. Using the efficient frontier, the farmer may choose an optimal solution that fits his/her risk-reward profile. 3 - Decision Assist Tool For Seed Variety To Provide Best Yield In Known Soil And Uncertain Future Weather Conditions Mehul Bansal, Robert Bosch Engineering and Business Solutions, Bengaluru, Karnataka, India, Mehul.Bansal@in.bosch.com Nataraj Vusirikala The gap between agriculture produce and demand is ever increasing due to growing world population. There is an urgent need for utilizing all possible methods and technology solutions to bridge this gap. One of the key challenges to increase the agricultural produce is the ability to take right decisions under uncertain climate and weather conditions. In this paper we discuss a method to provide decision assist to the farmer on the best variety of soybean seed to be sown at the start of a season. In order to optimize the yield under uncertain conditions, we use a combination of crop yield modeling, weather forecasting and portfolio optimization techniques to suggest best combination of soybean seed variety. The data used in this method is the historical soybean produce data and the corresponding soil and weather conditions under which the yield was produced, day-wise weather data (temperature, precipitation and solar radiation) at farm sites from 2008 to2014. We recommend planting the following varieties with the given percentages at site 2290 for year 2016: (i) 10% of Variety V107, (ii) 35% of Variety V179, (iii) 10% of Variety V189, (iv) 10% of Variety V193, and (v) 35% of Variety V46. SC15 104E-MCC Optimization and Learning in Biomedical Applications Invited: Modeling and Methodologies in Big Data Invited Session Chair: Mengdi Wang, Princeton University, NY, United States, mengdiw@princeton.edu 1 - Latent Graphical Models For Mixed Data Yang Ning, Princeton University, Princeton, NJ, United States, yning@exchange.Princeton.EDU, Jianqing Fan, Han Liu, Hui Zou Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this talk, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. 2 - Hierarchical Knowledge-gradient With Stochastic Binary Feedbacks With An Application In Personalized Health Care Yingfei Wang, Princeton University, Princeton, NJ, United States, yingfei@cs.princeton.edu, Warren B. Powell Motivated by personalized health care problems, we consider the problem of sequentially making decisions that are rewarded by ``successes’’ and ``failures’’ which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success. Our problem is motivated by healthcare applications where the highly sparsity makes leaning difficult. With the adaptation of an online boosting framework, we develop a knowledge-gradient (KG) policy to guide the experiment by maximizing the expected value of information. 3 - Approximate Newton-type Methods With Cubic Regularization Saeed Ghadimi, Princeton University, Princeton, NJ, United States, sghadimi@princeton.edu, Tong Zhang, Han Liu In this talk, we consider a class of second order methods for solving convex optimization problems. In particular, we propose Newton-type methods with cubic regularization when hessian of the objective function is not completely available. Convergence analysis of these methods under different conditions like stochastic setting are also presented.

SC14 104D-MCC Syngenta Crop Challenge in Analytics Invited: Agricultural Analytics Invited Session

Chair: Durai Sundaramoorthi, Washington University in Saint Louis, Campus Box 1156, One Brookings Drive, Saint Louis, MO, 63130- 4899, United States, dsundaramoorthi@gmail.com 1 - Hierarchical Modeling Of Soybean Variety Yield And Decision Making For Future Planting Plan Huaiyang Zhong, Stanford University, hzhong34@stanford.edu, Xiaocheng Li, David J Lovell We introduce a novel hierarchical machine learning mechanism for predicting soybean yield that can achieve a median absolute error of 3.74 bushels per acre in five-fold cross-validation. Further, we integrate this prediction mechanism with a weather forecasting model, and propose three different approaches for decision making under uncertainty to balance yield maximization and risk.

73