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We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…

Optimization and Control · Mathematics 2025-02-04 Nikolay Pogodaev , Maxim Staritsyn

Motivated by some applications in signal processing and machine learning, we consider two convex optimization problems where, given a cone $K$, a norm $\|\cdot\|$ and a smooth convex function $f$, we want either 1) to minimize the norm over…

Optimization and Control · Mathematics 2013-03-29 Zaid Harchaoui , Anatoli Juditsky , Arkadi Nemirovski

We investigate structural parameterizations of two identification problems: LOCATING-DOMINATING SET and TEST COVER. In the first problem, an input is a graph $G$ on $n$ vertices and an integer $k$, and one asks if there is a subset $S$ of…

Data Structures and Algorithms · Computer Science 2024-11-28 Dipayan Chakraborty , Florent Foucaud , Diptapriyo Majumdar , Prafullkumar Tale

This paper explores the fundamental properties of distributed minimization of a sum of functions with each function only known to one node, and a pre-specified level of node knowledge and computational capacity. We define the optimization…

Systems and Control · Computer Science 2012-10-26 Guodong Shi , Alexandre Proutiere , Karl Henrik Johansson

Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…

Optimization and Control · Mathematics 2020-04-22 Yu-HOng Dai , Liwei Zhang

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…

Optimization and Control · Mathematics 2020-07-23 Boris S. Mordukhovich , Pedro Pérez-Aros

When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…

Numerical Analysis · Mathematics 2024-09-04 Gabriele Ciaremalla , Tommaso Vanzan

$k$-defensive domination, a variant of the classical domination problem on graphs, seeks a minimum cardinality vertex set providing a surjective defense against any attack on vertices of cardinality bounded by a parameter $k$. The problem…

Discrete Mathematics · Computer Science 2020-10-09 Tınaz Ekim , Arthur Farley , Andrzej Proskurowski , Mordechai Shalom

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Optimization and Control · Mathematics 2021-06-15 Vladislav Tominin , Yaroslav Tominin , Ekaterina Borodich , Dmitry Kovalev , Alexander Gasnikov , Pavel Dvurechensky

Since the seminal papers by Giannessi, an interesting topic in vector optimization has been the characterization of (weak) efficiency thorough Minty and Stampacchia type variational inequalities. Several results have been proved to extend…

Optimization and Control · Mathematics 2016-12-02 Giovanni P. Crespi , Carola Schrage

This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…

Optimization and Control · Mathematics 2019-06-24 Constantin Christof , Gerd Wachsmuth

Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

In the present paper, the Polyak's principle, concerning convexity of the images of small balls through C1,1 mappings, is employed in the study of vector optimization problems. This leads to extend to such a context achievements of local…

Optimization and Control · Mathematics 2013-06-24 Amos Uderzo

We develop a new variational approach on level sets aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. With this new approach,…

Optimization and Control · Mathematics 2019-09-05 Daoli Zhu , Sien Deng

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

Data Structures and Algorithms · Computer Science 2020-09-22 Mark Sh. Levin

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…

Optimization and Control · Mathematics 2021-03-17 Tan H. Cao , Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…

Optimization and Control · Mathematics 2017-05-08 Nguyen Quang Huy , Do Sang Kim , Nguyen Van Tuyen

This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…

Optimization and Control · Mathematics 2025-11-25 Felipe Lara , Rishabh Pandey , Vinay Singh

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…

Quantum Physics · Physics 2025-07-22 Mateus Araújo , Andrew J. P. Garner , Miguel Navascues

In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…

Optimization and Control · Mathematics 2022-04-12 Wang Chen , Xinmin Yang , Yong Zhao