A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming

One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point … Read more

Distributions and Bootstrap for Data-based Stochastic Programming

In the context of optimization under uncertainty, we consider various combinations of distribution estimation and resampling (bootstrap and bagging) for obtaining samples used to acquire a solution and for computing a confidence interval for an optimality gap. This paper makes three experimental contributions to on-going research in data driven stochastic programming: a) most of the … Read more

Enhancing explainability of stochastic programming solutions via scenario and recourse reduction

Stochastic programming (SP) is a well-studied framework for modeling optimization problems under uncertainty. However, despite the significant advancements in solving large SP models, they are not widely used in industrial practice, often because SP solutions are difficult to understand and hence not trusted by the user. Unlike deterministic optimization models, SP models generally involve recourse … Read more

End-to-End Learning for Stochastic Optimization: A Bayesian Perspective

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk … Read more

New Formulations and Pricing Mechanisms for Stochastic Electricity Market Clearing Problem

We present new formulations of the stochastic electricity market clearing problem based on the principles of stochastic programming. Previous analyses have established that the canonical stochastic programming model effectively captures the relationship between the day-ahead and real-time dispatch and prices. The resulting quantities exhibit desirable guarantees of revenue adequacy, cost recovery, and price distortion in … Read more

Adaptive Importance Sampling Based Surrogation Methods for Bayesian Hierarchical Models, via Logarithmic Integral Optimization

We explore Maximum a Posteriori inference of Bayesian Hierarchical Models (BHMs) with intractable normalizers, which are increasingly prevalent in contemporary applications and pose computational challenges when combined with nonconvexity and nondifferentiability. To address these, we propose the Adaptive Importance Sampling-based Surrogation method, which efficiently handles nonconvexity and nondifferentiability while improving the sampling approximation of the … Read more

On the Regulatory and Economic Incentives for Renewable Hybrid Power Plants in Brazil

The complementarity between renewable generation profiles has been widely explored in the literature. Notwithstanding, the regulatory and economic frameworks for hybrid power plants add interesting challenges and opportunities for investors, regulators, and planners. Focusing on the Brazilian power market, this paper proposes a unified and isonomic firm energy certificate (FEC) calculation for non-controllable renewable generators, … Read more

Numerical Methods for Convex Multistage Stochastic Optimization

\(\) Optimization problems involving sequential decisions in  a  stochastic environment    were studied  in  Stochastic Programming (SP), Stochastic Optimal Control  (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP and  SOC modelling   approaches. In these frameworks there are natural situations  when the considered problems are  convex. Classical approach to sequential … Read more

Stochastic Programming Models for a Fleet Sizing and Appointment Scheduling Problem with Random Service and Travel Times

We propose a new stochastic mixed-integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following decision problems simultaneously: (i) a fleet sizing … Read more

Data-Driven Approximation of Contextual Chance-Constrained Stochastic Programs

Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more