This paper studies geometric and structural properties of quadratic multiobjective optimization problems. Thereby, a multiobjective optimization problem is called convexlike if the upper image, i.e., the image set plus the nonnegative orthant, is a convex set. Moreover, we say that a feasible point is supported in case it is a minimal solution of a weighted … Read more
Physics-Inspired Graph Neural Networks (PI-GNNs) reformulate MAX-CUT as QUBO energy minimization, training a GNN to produce soft binary node assignments without labeled data. The baseline PI-GCN uses static, degree-normalized aggregation, while its attention-augmented counterpart PI-GAT—built on GATv2—introduces additional hyperparameters whose effects remain uncharacterized. This paper addresses that gap through controlled experiments on five Gset benchmark … Read more
The diverse constraints of industrial applications lead to variants of two-dimensional (2D) irregular packingproblems that require tailored solution methods. This paper addresses a real-world industrial challenge byproposing a new problem definition, the maximum reusable contiguous area problem (MRCAP), and a novelmetric, the maximum contiguous area, to measure and maximize the contiguous unused area in a … Read more
We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more
We study tight conic relaxations for a quadratically constrained quadratic programming (QCQP) formulation of rank-one doubly nonnegative (DNN) matrix completion. Motivated by sparse QCQPs whose lifted matrix variables include elements not directly specified by the objective or constraints, we interpret tightness as a rank-one completion property for the unspecified elements. For sparsity patterns whose blocks … Read more
Infinite-horizon risk-sensitive Markov decision processes (MDPs) under the discounted cost criterion are challenging to solve because the optimal policy may be nonstationary. Existing methods typically reformulate the problem as a continuous-state risk-neutral MDP and rely on state discretization or value-function approximation, often without explicit stopping conditions or error bounds. In this paper, we present approximate … Read more
Direct Multisearch (DMS) is a class of direct-search algorithms designed for multiobjective derivative-free optimization. Its framework consists of an optional search step and a poll step, the latter ensuring the corresponding theoretical convergence properties. Recently, a search strategy based on the minimization of quadratic polynomial models, constructed from previously evaluated points, was proposed to improve … Read more
We consider a contextual stochastic optimization (CSO) problem, where one has observations of the uncertain parameters together with concurrent observations of covariates, and the goal is to choose decisions that minimize expected cost conditioned on new covariate observations. The empirical residuals-based sample average approximation (ER-SAA) of the CSO problem constructs scenarios of uncertainty by combining … Read more
Our project investigates replacing the classical adversarial discriminator in GAN training with a kernel-based distance metric, namely Kernel Stein Discrepancy (KSD). We assess whether a kernelized objective can improve training stability and efficiency without compromising sample quality, and we evaluate accelerated Nystrom approximations with Renyi landmark selection on CIFAR-10. ArticleDownload View PDF
Primal heuristics for finding high-quality feasible solutions are an important component in mixed-integer optimization (MIO) solvers. Recent advances in GPU-accelerated optimization algorithms show the potential of GPU acceleration for continuous optimization. In this paper, we introduce the Parallel Node Generation and Exploration Algorithm (PaNGEA), a GPU-friendly MIO primal heuristic. PaNGEA explores restricted subproblems by combining … Read more