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
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
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
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
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 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
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic, and constraint function and derivative values can be computed explicitly, but the objective function is stochastic. It is assumed in this setting that it … Read more
When considering the design of electricity-intensive industrial processes, a challenge is that future electricity prices are highly uncertain. Design decisions made before construction can affect operations decades into the future. We thus explore whether including electricity price uncertainty into the design process affects design decisions. We apply stochastic optimization to the design and operations of … Read more
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for such problems. However, quantifying the uncertainty associated with the underlying training algorithm is not well-studied in the non-convex setting. In order to address this short-coming, in this work, … Read more
Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity (the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard), practical instances of the problem usually involve a large to very large number of decision variables, typically of the order … Read more