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We investigate the computational complexity of min-max optimization under coupled constraints. The work of Daskalakis, Skoulakis, and Zampetakis [DSZ21] was the first to study min-max optimization through the lens of computational…
We study the universal closest refinement problem on measurable bipartite relations over standard Borel spaces. Given prescribed side measures, the feasible class consists of finite refinement plans concentrated on the relation and carrying…
When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Obtaining object response maps is one important step to achieve weakly-supervised semantic segmentation using image-level labels. However, existing methods rely on the classification task, which could result in a response map only attending…
This paper considers the linear objective function optimization with respect to a novel system of fuzzy relation equations, where the fuzzy compositions are defined by the minimum t-norm. It is proved that the feasible solution set is…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…
In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of generalized hybrid mappings in a Hilbert space. Our results…
As explained in detail in the prologue to this manuscript, boundedness of weak solutions for general classes of elliptic equations in divergence form is a classic tool for achieving higher regularity. We propose here some global boundedness…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
In recent developments, a novel set of necessary optimality conditions for mixed constrained optimal control problems, termed the asymptotic weak maximum principle, has been formulated. These novel conditions deviate from the classical ones…
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…
We introduce Integrated Weak Learning, a principled framework that integrates weak supervision into the training process of machine learning models. Our approach jointly trains the end-model and a label model that aggregates multiple…
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
The generalized Nash equilibrium problems play a significant role in modeling and analyzing several complex economics problems. In this work, we consider jointly convex generalized Nash games which were introduced by Rosen. We study two…
We develop sensitivity analyses for weak nulls in matched observational studies while allowing unit-level treatment effects to vary. The methods may be applied to studies using any optimal without-replacement matching algorithm. In contrast…