Consider settings such as stochastic optimization where a smooth objective function $f$ is unknown but can be estimated with an \emph{inexact oracle} such as quasi-Monte Carlo (QMC) or numerical quadrature. The inexact oracle is assumed to yield function estimates having error that decays with increasing oracle effort. For solving such problems, we present the Adaptive … Read more
We present a stochastic model predictive control (MPC) framework to determine real-time commitments in energy and frequency regulation markets for a stationary battery system while simultaneously mitigating long-term demand charges for an attached load. The framework solves a two-stage stochastic program over a receding horizon that maximizes the expected profit and that factors in uncertainty … Read more
We devise an algorithm for finding the global optimal solution of the so-called optimal power flow problem (OPF) for a class of power networks with a tree topology, also called radial networks, for which an efficient and reliable algorithm was not previously known. The algorithm we present is called the tree reduction/expansion method, and is … Read more
We introduce two new weaker Constraint Qualifications (CQs) for Mathematical Programs with Equilibrium (or Complementarity) Constraints, MPEC for short. One of them is a tailored version of the Constant Rank of Subspace Component (CRSC) and the other is a relaxed version of the MPEC-No Nonzero Abnormal Multiplier Constraint Qualification (MPEC-NNAMCQ). Both incorporate the exact set … Read more
We study the problem of choosing the best subset of p features in linear regression given n observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem either by combining the two objectives using … Read more
This paper examines the impacts of governmental incentives for coal-fired power plants to generate renewable energy via biomass cofiring technology. The most common incentive is the production tax credit (PTC), a flat rate reimbursement for each unit of renewable energy generated. The work presented here proposes PTC alternatives, incentives that are functions of plant capacity … Read more
In this paper, we analyze in depth a simplicial decomposition like algorithmic framework for large scale convex quadratic programming. In particular, we first propose two tailored strategies for handling the master problem. Then, we describe a few techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments on both real … Read more
In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we … Read more
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to select the most relevant Benders cuts. We propose a limited memory variant of Level 1 and show the convergence of DDP … Read more
We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates strategies to select the most relevant cuts of the approximate recourse functions. We prove the convergence of the method in a finite number of iterations and use it to solve … Read more