In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as symmetry and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport … Read more
Piezoelectric material behavior is mathematically described by coupled hyperbolic-elliptic partial differential equations (PDEs) governing mechanical displacement and electrical potential. This paper presents advancements in the theory of identifying material parameters in piezoelectric PDEs. We focus on modeling and analyzing the inverse problem assuming matrix-valued Sobolev-Bochner parameters to encompass a time and space-dependent setting and thus … Read more
Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized Wasserstein distance, referred to as Sinkhorn DRO. Existing work primarily addresses Sinkhorn DRO from a dual perspective, leveraging its formulation as a conditional stochastic optimization … Read more
This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden (RSE-PSB) method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. The approximation of the symmetric, yet potentially indefinite, second-order term, which is neglected by standard Levenberg-Marquardt (LM) approaches, integrates regularization and structure exploitation directly within the Quasi-Newton (QN) framework, … Read more
Controlling the dynamics of large-scale networks is essential for a macroscopic reduction of overall consumption and losses in the context of energy supply, finance, logistics, and mobility. We investigate the optimal control of semilinear dynamical systems on asymptotically infinite networks, using the notion of graphons. Graphons represent a limit object of a converging graph sequence … Read more
In this paper, we study the two-stage distributionally robust optimization (DRO) problem from the primal perspective. Unlike existing approaches, this perspective allows us to build a deeper and more intuitive understanding on DRO, to leverage classical and well established solution methods and to develop a general and fast decomposition algorithm (and its variants), and to … Read more
Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the … Read more
We consider a feature-based personalized pricing problem in which the buyer is strategic: given the seller’s pricing policy, the buyer can augment the features that they reveal to the seller to obtain a low price for the product. We model the seller’s pricing problem as a stochastic program over an infinite-dimensional space of pricing policies … Read more
In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset, which realizes the distance between the subsets. We discuss the problem in more general normed … Read more
Low-carbon societies will need to store vast amounts of electricity to balance intermittent generation from wind and solar energy, for example, through frequency regulation. Here, we derive an analytical solution to the decision-making problem of storage operators who sell frequency regulation power to grid operators and trade electricity on day-ahead markets. Mathematically, we treat future … Read more