ICCOPT2025USC

Session: Optimization Method Generation with Large Language Models
Chair: Xiangfeng Wang
Cluster: Optimization for Emerging Technologies (LLMs, Quantum Computing, ...)

Talk 1: Generative Models in Reinforcement Learning
Speaker: Wenhao Li
Abstract: ~

Talk 2: LLM-based Simulation Optimization
Speaker: Jun Luo
Abstract: ~

Talk 3: LLM-based Optimization Method for Scheduling
Speaker: Xiangfeng Wang
Abstract: ~

Session: Applications of polynomial optimization to data analysis II
Chair: Yong Sheng Soh
Cluster: Conic and Semidefinite Optimization

Talk 1: Semidefinite Network Games
Speaker: Antonios Varvitsiotis
Abstract: Network games are an important class of games that model agent interactions in networked systems, where players are situated at the nodes of a graph and their payoffs depend on the actions taken by their neighbors. We extend the classical framework by considering a game model where the strategies are positive semidefinite matrices having trace one. These (continuous) games can serve as a simple model of quantum strategic interactions. We focus on the zero-sum case, where the sum of all players’ payoffs is equal to zero. We establish that in this class of games, Nash equilibria can be characterized as the projection of a spectrahedron, that is, the feasible region of a semidefinite program. Furthermore, we demonstrate that determining whether a game is a semidefinite network game is equivalent to deciding if the value of a semidefinite program is zero. Beyond the zero-sum case, we characterize Nash equilibria as the solutions of a semidefinite linear complementarity problem.

Talk 2: (Moved to 4K)Sum of squares hierarchy for the Gromov-Wasserstein Problem
Speaker: Yong Sheng Soh
Abstract: (Moved to 4K)The Gromov-Wasserstein (GW) Problem is an extension of the classical optimal transport problem that allows one to compute distances between probability distributions specified over incomparable metric spaces. Broadly speaking, to get around the lack of a natural notion of distance between objects residing in different metric spaces, the GW computes the minimum of a suitably defined objective taken over all possible embeddings of the input metric spaces to a common space. This process leaves us with solving a non-convex quadratic programming instance. In this talk, we discuss the ideas of the sum-of-squares hierarchy applied to solving the GW problem. As a note, the central object of interest in the GW problem is a probability distribution, and we describe the necessary language in which ideas of polynomial optimization carry through to distributions.

Talk 3: On the geometric and computational complexity of polynomial bilevel optimization
Speaker: Quoc-Tung Le
Abstract: Bilevel optimization is an important mathematical tool to model phenomena in many domains, such as economic game theory, decision science and machine learning, to name but a few. Despite its importance, efficient and scalable algorithms for bilevel optimization are mostly developed for the (strong) convexity of the lower-level problem case, which is unrealistic for many practical tasks. In the quest to understand more general bilevel problems, we relax the lower level strong convexity and consider polynomial bilevel optimization, i.e., polynomial objective functions and constraints. We focus on the worst-case analysis of this class of problems, from both geometric and computational viewpoints. Our analysis suggests that even the algebraic rigidity of polynomials does not exclude extreme pathologies induced by the bilevel optimization. More specifically, we demonstrate that any semi-algebraic function can be represented as the objective of a polynomial bilevel problem. This discovery implies that solving polynomial bilevel optimization is equivalent to optimizing general semi-algebraic functions. We obtain other sharp variations of this result by considering relevant properties of the lower problem, such as convexity or feasible set compacity. In addition, we show the Σ2p-hardness of polynomial bilevel optimization, characterizing polynomial bilevel problems as vastly more challenging than NP-complete problems (under reasonable hardness assumptions).

Session: Optimization Applications in Energy Systems
Chair: Sungho Shin
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)

Talk 1: Multiperiod Optimization for Power Grid Applications
Speaker: Mihai Anitescu
Abstract: There has been a growing interest in solving multi-period AC OPF problems, as the increasingly fluctuating electricity market requires operation planning over multiple periods. These problems, formerly deemed intractable, are now becoming technologically feasible to solve thanks to the advent of high-memory GPU hardware and accelerated NLP tools. This study evaluates the capability of the ExaModels.jl and MadNLP.jl tools for GPU-centered nonlinear programming to tackle previously unsolvable multi-period AC OPF instances. Our numerical experiments, run on an NVIDIA GH200, demonstrate that we can solve a multi-period OPF instance with more than 10 million variables up to 10−4 precision in less than 10 minutes.

Talk 2: Optimal Power Flow Under Constraint-Informed Uncertainty
Speaker: Anirudh Subramanyam
Abstract: Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to DC Optimal Power Flow (DC-OPF) problems, developing a novel approach to uncertainty modeling. Current methods tackle these problems by first modeling random variables using high-dimensional statistical distributions that scale with the number of system buses, followed by deriving convex reformulations of the probabilistic constraints. We propose an alternative methodology that uses the probabilistic constraints themselves to inform the structure of uncertainty, enabling significant dimensionality reduction. Rather than learning joint distributions of wind generation forecast errors across all units, we model two key distributions: system-wide aggregate forecast errors and individual unit errors weighted by transmission line flow sensitivities. We evaluate our approach under both Gaussian and non-Gaussian uncertainty distributions, demonstrating improvements over state-of-the-art in both statistical accuracy and optimization performance.

Talk 3: Characterizing marginal value of storage in distribution grid operations
Speaker: Dirk Lauinger
Abstract: Electricity distribution companies invest in storage to shave peak load and reduce investments into substation and distribution line upgrades. In deregulated electricity markets, storage assets owned by distribution companies are not allowed to participate in electricity markets, which leads to the assets sitting idle most of the time. Contracting for storage could provide investors with additional value streams, distribution companies with cheaper storage, and rate payers with reduced prices. We integrate contracted storage into distribution company investment planning problems and find that peak shaving reduces profits from market participation by about 1% in a Massachusetts case study. Capital investment savings from contracted storage more than compensate for this reduction. Both distribution companies and storage investors could thus benefit from contracted storage.