First- and Second-Order High Probability Complexity Bounds for Trust-Region Methods with Noisy Oracles

In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value is computed with noise and for which gradient and Hessian estimates are inexact and possibly random. In order to account for the noise, the method utilizes a relaxed step acceptance criterion and a cautious trust-region radius … Read more

Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

In this paper, we propose a stochastic variance reduction method for solving equality constrained optimization problems. Specifically, we develop a method based on the sequential quadratic programming paradigm that utilizes gradient approximations via predictive variance reduction techniques. Under reasonable assumptions, we prove that a measure of first-order stationarity evaluated at the iterates generated by our … Read more

Intraday Power Trading: Towards an Arms Race in Weather Forecasting?

We propose the first weather-based algorithmic trading strategy on a continuous intraday power market. The strategy uses neither production assets nor power demand and generates profits purely based on superior information about aggregate output of weather-dependent renewable production. We use an optimized parametric policy based on state-of-the-art intraday updates of renewable production forecasts and evaluate … Read more

Convergence rates of the stochastic alternating algorithm for bi-objective optimization

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating … Read more

Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is … Read more

Stochastic Look-Ahead Commitment: A Case Study in MISO

This paper introduces the Stochastic Look Ahead Commitment (SLAC) software prototyped and tested for the Midcontinent Independent System Operator (MISO) look ahead commitment process. SLAC can incorporate hundreds of wind, load and net scheduled interchange (NSI) uncertainty scenarios. It uses a progressive hedging method to solve a two-stage stochastic unit commitment. The first stage optimal … Read more

Adaptive Sampling Quasi-Newton Methods for Zeroth-Order Stochastic Optimization

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic function using finite differences within a common random number framework. We develop modified versions of a norm … Read more

SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm

A wide class of problems involves the minimization of a coercive and differentiable function $F$ on $\mathbb{R}^N$ whose gradient cannot be evaluated in an exact manner. In such context, many existing convergence results from standard gradient-based optimization literature cannot be directly applied and robustness to errors in the gradient is not necessarily guaranteed. This work … Read more

Decision Intelligence for Nationwide Ventilator Allocation

Many states in the U.S. have faced shortages of medical resources because of the surge in the number of patients suffering from COVID-19. As many projections indicate, the situation will be far worse in coming months. The upcoming challenge is not only due to the exponential growth in cases but also because of inherent uncertainty … Read more

Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is assumed that constraint function and derivative values can be computed, but that only stochastic approximations are available for the objective function and its … Read more