## 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

## A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians

A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, … Read more

## LSOS: Line-search Second-Order Stochastic optimization methods for nonconvex finite sums

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at … Read more

## Stochastic Variance-Reduced Prox-Linear Algorithms for Nonconvex Composite Optimization

We consider the problem of minimizing composite functions of the form \$f(g(x))+h(x)\$, where~\$f\$ and~\$h\$ are convex functions (which can be nonsmooth) and \$g\$ is a smooth vector mapping. In addition, we assume that \$g\$ is the average of finite number of component mappings or the expectation over a family of random component mappings. We propose … Read more

## Kernel Distributionally Robust Optimization

We propose kernel distributionally robust optimization (Kernel DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct a wide range of convex ambiguity sets, including sets based on integral probability metrics and finite-order moment bounds. This perspective unifies multiple existing robust and stochastic optimization … Read more

## A Primal-Dual Algorithm for Risk Minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is … Read more

## Fleet Sizing and Allocation for On-demand Last-Mile Transportation Systems

The last-mile problem refers to the provision of travel service from the nearest public transportation node to home or other destination. Last-Mile Transportation Systems (LMTS), which have recently emerged, provide on-demand shared transportation. In this paper, we investigate the fleet sizing and allocation problem for the on-demand LMTS. Specifically, we consider the perspective of a … Read more

## A General Framework for Optimal Data-Driven Optimization

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be expressed as the minimizer of a surrogate optimization model constructed from the data. The quality of a data-driven decision … Read more

## A Noise-Tolerant Quasi-Newton Method for Unconstrained Optimization

This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or are subject to statistical noise. The classical BFGS and L-BFGS methods can fail in such circumstances because the updating procedure … Read more

## Robot Dance: a mathematical optimization platform for intervention against Covid-19 in a complex network

Robot Dance is a computational platform developed in response to the coronavirus outbreak, to support the decision making on public policies at a regional level. The tool is suitable for understanding and suggesting levels of intervention needed to contain the spread of diseases when the mobility of inhabitants through a regional network is a concern. … Read more