Data collection in application domains like agriculture and environmental science requires the deployment of sensors in large remote areas. These use cases challenge the traditional optimal experimental design (OED) formulation from statistics by their scale as well as the presence of complex operational constraints, such as that data is collected along the trajectory of a … Read more
We consider a capacitated location-allocation-pricing problem in a single-commodity supply chain with stochastic price-sensitive demands, where the location, allocation and pricing decisions are made simultaneously. Under a general risk measure representing an arbitrary risk tolerance policy, the problem is modeled as a two-stage stochastic mixed-integer program with a translation-invariant monotone risk measure. To solve the … Read more
Parameter estimation is a fundamental challenge in machine learning, crucial for tasks such as neural network weight fitting and Bayesian inference. This paper focuses on the complexity of estimating translation μ∈R^l and shrinkage σ∈R++ parameters for a distribution of the form (1/sigma^l) f_0((x−μ)/σ), where f_0 is a known density in R^l given n samples. We … Read more
We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization method (SM), where the iterates of an asymptotically convergent iterative feasibility-seeking algorithm are perturbed by objective function nonascent steps. We investigate the question under what conditions a sequence generated by an SM … Read more
Antibiotic resistance, which is a serious healthcare issue, emerges due to uncontrolled and repeated antibiotic use that causes bacteria to mutate and develop resistance to antibiotics. The Antibiotics Time Machine Problem aims to come up with treatment plans that maximize the probability of reversing these mutations. Motivated by the severity of the problem, we develop … Read more
Explainable artificial intelligence is one of the most important trends in modern machine-learning research. The idea is to explain the outcome of a model by presenting a certain change in the input of the model so that the outcome changes significantly. In this paper, we study this question for linear optimization problems as an automated … Read more
Accelerated proximal gradient methods have become a useful tool in large-scale convex optimization, specially for variational regularization with non-smooth priors. Prevailing convergence analysis considers that users can perform the proximal and the gradient steps exactly. Still, in some practical applications, the proximal or the gradient steps must be computed inexactly, which can harm convergence speed … Read more
The Alternating Direction Method of Multipliers (ADMM) is widely recognized for its efficiency in solving separable optimization problems. However, its application to optimization on Riemannian manifolds remains a significant challenge. In this paper, we propose a novel inertial Riemannian gradient ADMM (iRG-ADMM) to solve Riemannian optimization problems with nonlinear constraints. Our key contributions are as … Read more
The increasing penetration of renewable energy into power systems necessitates the development of effective methodologies to integrate initially disconnected generation sources into the grid. This paper introduces the Longest Shortest-Path-Connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of Transmission Expansion Planning (TEP) using valid inequalities (VIs). Traditional approaches for … Read more
We present a novel framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP). The CLRP is a classical yet NP-hard problem that integrates strategic facility location with operational vehicle routing decisions, aiming to simultaneously minimize both fixed and variable costs. The proposed method first trains a permutationally invariant neural … Read more