Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these estimators as the sample size goes to infinity, which is both of theoretical as well as practical interest. This area of … Read more

Monotonicity and Complexity of Multistage Stochastic Variational Inequalities

In this paper, we consider multistage stochastic variational inequalities (MSVIs). First, we give multistage stochastic programs and multistage multi-player noncooperative game problems as source problems. After that, we derive the monotonicity properties of MSVIs under less restrictive conditions. Finally, the polynomial rate of convergence with respect to sample sizes between the original problem and its … Read more

Spectral Projected Subgradient Method for Nonsmooth Convex Optimization Problems

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves … Read more

A Prescriptive Machine Learning Method for Courier Scheduling on Crowdsourced Delivery Platforms

Crowdsourced delivery platforms face the unique challenge of meeting dynamic customer demand using couriers not employed by the platform. As a result, the delivery capacity of the platform is uncertain. To reduce the uncertainty, the platform can offer a reward to couriers that agree to be available to make deliveries for a specified period of … Read more

Minimizing Nonsmooth Convex Functions with Variable Accuracy

We consider unconstrained optimization problems with nonsmooth and convex objective function in the form of mathematical expectation. The proposed method approximates the objective function with a sample average function by using different sample size in each iteration. The sample size is chosen in an adaptive manner based on the Inexact Restoration. The method uses line … Read more

Data-driven sample average approximation with covariate information

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to choose a decision that minimizes the expected cost conditioned on this observation. We investigate three data-driven frameworks that integrate a machine learning … Read more

On sample average approximation for two-stage stochastic programs without relatively complete recourse

We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible recourse action. As a feasibility measure of the SAA solution, we consider the “recourse likelihood”, which is the probability that the solution has … Read more

Sample Average Approximation for Stochastic Nonconvex Mixed Integer Nonlinear Programming via Outer Approximation

Stochastic mixed-integer nonlinear programming (MINLP) is a very challenging type of problem. Although there have been recent advances in developing decomposition algorithms to solve stochastic MINLPs, none of the existing algorithms can address stochastic MINLPs with continuous distributions. We propose a sample average approximation-based outer approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs … Read more

Transmission Switching Under Wind Uncertainty Using Linear Decision Rules

Increasing penetration of wind and renewable generation poses significant challenges to the power system operations and reliability. This paper considers the real-time optimal transmission switching (OTS) problem for determining the generation dispatch and network topology that can account for uncertain energy resources. To efficiently solve the resultant two-stage stochastic program, we propose a tractable linear … Read more

Improving sample average approximation using distributional robustness

We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sample performance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under … Read more