On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

Categories Stochastic Programming

We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the … Read more

Fast Robust Methods for Singular State-Space Models

Categories Control Applications, Nonsmooth Optimization, Statistics Tags , ,

State-space models are used in a wide range of time series analysis applications. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a broad range of optimization formulations to allow outlier-robust estimation, as well as constraints to capture prior information. Here we … Read more

Admissibility of solution estimators for stochastic optimization

Categories Stochastic Programming Tags , , ,

We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for … Read more

Hybrid Rebalancing with Dynamic Hubbing for Free-floating Bike Sharing Using Multi-objective Simulation Optimization

Categories Optimization of Simulated Systems, Transportation Tags , , , ,

For rebalancing problem of free-floating bike sharing systems, we propose dynamic hubbing (i.e. dynamically determining geofencing areas) and hybrid rebalancing (combining user-based and operator-based strategies) and solve the problem with a novel multi-objective simulation optimization approach. Given historical usage data and real-time bike GPS location information, dynamic geofenced areas (hubs) are determined to encourage users … Read more

Discrete Approximation Scheme in Distributionally Robust Optimization

Categories Robust Optimization Tags , , , ,

Discrete approximation which is the prevailing scheme in stochastic programming in the past decade has been extended to distributionally robust optimization (DRO) recently. In this paper we conduct rigorous quantitative stability analysis of discrete approximation schemes for DRO, which measures the approximation error in terms of discretization sample size. For the ambiguity set defined through … Read more

Local Rapid Learning for Integer Programs

Categories Integer Programming Tags , , , ,

Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is applied at the root to learn … Read more

A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming

Categories (Mixed) Integer Nonlinear Programming Tags , , ,

Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and … Read more

An Augmented Lagrangian Method for Quasi-Equilibrium Problems

Categories Nonlinear Optimization

In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global … Read more

Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints

Categories Nonlinear Systems and Least-Squares Tags , , ,

Given a twice-continuously differentiable vector-valued function $r(x)$, a local minimizer of $\|r(x)\|_2$ within a convex set is sought. We propose and analyse tensor-Newton methods, in which $r(x)$ is replaced locally by its second-order Taylor approximation. Convergence is controlled by regularization of various orders. We establish global convergence to a constrained first-order critical point of $\|r(x)\|_2$, … Read more

Towards an efficient Augmented Lagrangian method for convex quadratic programming

Categories Constrained Nonlinear Optimization, Linear Programming, Quadratic Programming Tags , , , ,

Interior point methods have attracted most of the attention in the recent decades for solving large scale convex quadratic programming problems. In this paper we take a different route as we present an augmented Lagrangian method for convex quadratic programming based on recent developments for nonlinear programming. In our approach, box constraints are penalized while … Read more