PyMOSO: Software for Multi-Objective Simulation Optimization with R-PERLE and R-MinRLE

Categories Optimization of Simulated Systems, Optimization Software and Modeling Systems Tags ,

We present the PyMOSO software package for (1) solving multi-objective simulation optimization (MOSO) problems on integer lattices, and (2) implementing and testing new simulation optimization (SO) algorithms. First, for solving MOSO problems on integer lattices, PyMOSO implements R-PERLE, a state-of-the-art algorithm for two objectives, and R-MinRLE, a competitive benchmark algorithm for three or more objectives. … Read more

On the Convergence to Stationary Points of Deterministic and Randomized Feasible Descent Directions Methods

Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

We study the class of nonsmooth nonconvex problems in which the objective is to minimize the difference between a continuously differentiable function (possibly nonconvex) and a convex (possibly nonsmooth) function over a convex polytope. This general class contains many types of problems, including difference of convex functions (DC) problems, and as such, can be used … Read more

A convex integer programming approach for optimal sparse PCA

Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming

Principal component analysis (PCA) is one of the most widely used dimensionality reduction tools in scientific data analysis. The PCA direction, given by the leading eigenvector of a covariance matrix, is a linear combination of all features with nonzero loadings—this impedes interpretability. Sparse principal component analysis (SPCA) is a framework that enhances interpretability by incorporating … Read more

Understanding the Acceleration Phenomenon via High-Resolution Differential Equations

Categories Convex Optimization, Global Optimization Theory, Unconstrained Optimization Tags ,

Gradient-based optimization algorithms can be studied from the perspective of limiting or- dinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distin- guish between two fundamentally different algorithms—Nesterov’s accelerated gradient method for strongly convex functions (NAG-SC) and Polyak’s heavy-ball method—we study an alter- native limiting process that yields high-resolution ODEs. We … Read more

Exploiting Partial Correlations in Distributionally Robust Optimization

Categories Polyhedra, Robust Optimization, Semi-definite Programming Tags , , ,

In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more

Convergence Rate Analysis of a Stochastic Trust Region Method via Supermartingales

Categories Nonlinear Optimization Tags , ,

We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analysing properties of an underlying generic stochastic process, in particular by deriving a bound on the expected stopping time of this process. We utilise this framework to analyse the bounds on expected global … Read more

Condition Number Analysis of Logistic Regression, and its Implications for Standard First-Order Solution Methods

Categories Convex Optimization, Data-Mining, Statistics Tags , , ,

Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is … Read more

Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning

Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more

Dynamic Courier Routing for a Food Delivery Service

Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Transportation

Services like Grubhub and UberEats have revolutionized the way that diners can find and order from restaurants. The standard business model for such services, however, allows diners to order from only one restaurant at a time. Inspired by a food delivery service in the southeastern United States, this paper proposes the framework for a more … Read more

Scalable Branching on Dual Decomposition of Stochastic Mixed-Integer Programming Problems

Categories (Mixed) Integer Linear Programming, Parallel Algorithms, Stochastic Programming

We present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caro e and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including 1) branching on the optimal solutions … Read more