arXiv subjects

Dimitri Papageorgiou

Publications and source records attributed to Dimitri Papageorgiou.

3 recordsLinked to original sources

arXiv2024

Solution Polishing via Path Relinking for Continuous Black-Box Optimization

When faced with a limited budget of function evaluations, state-of-the-art black-box optimization (BBO) solvers struggle to obtain globally, or sometimes even locally, optimal solutions. In such cases, one may pursue solution polishing, i.e., a computational method to improve (or ``polish'') an incumbent solution, typically via some sort of evolutionary algorithm involving two or more solutions. While solution polishing in ``white-box'' optimization has existed for years, relatively little has been published regarding its application in costly-to-evaluate BBO. To fill this void, we explore two novel methods for performing solution polishing along one-dimensional curves rather than along straight lines. We introduce a convex quadratic program that can generate promising curves through multiple elite solutions, i.e., via path relinking, or around a single elite solution. In comparing four solution polishing techniques for continuous BBO, we show that solution polishing along a curve is competitive with solution polishing using a state-of-the-art BBO solver.

math.OC↗

arXiv2023

Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming

Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the players' decision problems, they only apply as heuristic methods when the players are modeled by nonconvex optimization problems. In contrast, this work approaches generalized Nash equilibrium using theory and methods for the global optimization of nonconvex bilevel programs. Through this perspective, we draw precise connections between generalized Nash equilibria, feasibility for bilevel programming, the Nikaido-Isoda function, and classic arguments involving Lagrangian duality and spatial price equilibrium. Significantly, this is all in a general setting without the assumption of convexity. Along the way, we introduce the idea of minimum disequilibrium as a solution concept that reduces to traditional equilibrium when equilibrium exists. The connections with bilevel programming and related semi-infinite programming permit us to adapt global optimization methods for those classes of problems, such as constraint generation or cutting plane methods, to the problem of finding a minimum disequilibrium solution. We propose a specific algorithm and show that this method can find a pure Nash equilibrium even when the players are modeled by mixed-integer programs.

math.OC↗

arXiv2018

Active Metric Learning for Supervised Classification

Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated "target neighbors," "triplets," and "similarity pairs." Another salient feature of our method is its ability to enable active learning by recommending precise regions to sample after an optimal metric is computed to improve classification performance. This targeted acquisition can significantly reduce computational burden by ensuring training data completeness, representativeness, and economy. We demonstrate classification and computational performance of the algorithms through several simple and intuitive examples, followed by results on real image and medical datasets.

cs.LG↗