The paper presents a three-phase algorithm to compute the set of nondominated points for the binary version of the uncapacitated facility location problem with two objectives. The first phase constructs a paving in objective space which is a collection of boxes that covers all nondominated points. The paving procedure is a branch and bound algorithm … Read more
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly subsidies are commonly required. We propose a new pricing scheme for nonconvex markets with both discreteness and nonlinearity, by convexifying nonconvex structures through a semidefinite … Read more
In this work we develop and analyze a semi-smooth Newton method for the general non- linear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear mapping. We generalize Robinson’s normal equations to a conic setting, yielding what we call the … Read more
We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes a nest of conditional expectations and nonlinear cost functions. It has numerous applications and arises, for example, in optimal stopping, linear-quadratic regulator problems, distributionally robust contextual bandits, … Read more
Given a simple graph G = (V, E) with edge cost c ∈ ℝ^|E|, a positive integer h, source s ∈ V and terminal t ∈ V, the hop-constrained cheapest path problem (HCCP) seeks to find an s–t path of length at most h hops with the cheapest cost. This paper proposes a cut-based mixed … Read more
A unified framework for first-order optimization algorithms for nonconvex unconstrained optimization is proposed that uses adaptively preconditioned gradients and includes popular methods such as full and diagonal AdaGrad, AdaNorm, as well as adpative variants of Shampoo and Muon. This framework also allows combining heterogeneous geometries across different groups of variables while preserving a unified convergence … Read more
In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components … Read more
We study the variational convergence of robust integral functionals induced by empirical probability measures. We establish a generalized consistency framework where the ambiguity set is constructed using a probability metric. By replacing traditional uniform equicontinuity assumptions with inherent convexity and general probability metric domination, we prove the almost sure pointwise and uniform convergence of the … Read more
We study computational aspects of a key problem in robust statistics—the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and … Read more
We present a machine learning (ML) component designed to enhance the well-known branch-and-cut (B&C) framework for the symmetric traveling salesman problem (TSP) in which only the subtour elimination constraints (SECs) violated by previously found integer solutions are considered. The objective of the ML component is to identify which SECs, from a pool of candidates, will … Read more