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A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…

Robotics · Computer Science 2023-09-26 Patrick Zhong , Federico Rossi , Dylan A. Shell

The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonconvex vector optimization problems with unbounded constraint set via asymptotic cones and…

Optimization and Control · Mathematics 2025-10-14 Tran Van Nghi , Le Ngoc Kien , Nguyen Van Tuyen

The paper concerns multiobjective linear optimization problems in R^n that are parameterized with respect to the right-hand side perturbations of inequality constraints. Our focus is on measuring the variation of the feasible set and the…

Optimization and Control · Mathematics 2019-07-24 María J. Cánovas , Marco A. López , Boris Mordukhovich , Juan Parra

We present a method for proving the existence of solutions to a class of one dimensional variational problems. The method is demonstrated by two examples of optimal interpolation problems which are motivated by engineering applications. In…

Differential Geometry · Mathematics 2014-02-25 Philip Schrader

This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…

Optimization and Control · Mathematics 2025-02-19 Chuang-liang Zhang , Yun-cheng Liu , Nan-jing Huang

We propose a model of Pareto optimization (multi-objective programming) in the context of a categorical theory of resources. We describe how to adapt multi-objective swarm intelligence algorithms to this categorical formulation.

Category Theory · Mathematics 2022-04-27 Matilde Marcolli

Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the…

Probability · Mathematics 2010-12-06 Alexander Nazarov , Natalia Stepanova

We prove a necessary stationary condition for non-differentiable isoperimetric variational problems with scale derivatives, defined on the class of H\"{o}lder continuous functions.

Optimization and Control · Mathematics 2009-07-17 Ricardo Almeida , Delfim F. M. Torres

Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…

Optimization and Control · Mathematics 2025-02-25 William W. Hager

The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…

Information Theory · Computer Science 2010-08-24 Urs Niesen , Devavrat Shah , Gregory Wornell

We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…

Optimization and Control · Mathematics 2019-06-17 Ana P. Lemos-Paiao , Cristiana J. Silva , Delfim F. M. Torres

Constrained single-objective problems have been frequently tackled by evolutionary multi-objective algorithms where the constraint is relaxed into an additional objective. Recently, it has been shown that Pareto optimization approaches…

Neural and Evolutionary Computing · Computer Science 2024-06-10 Frank Neumann , Carsten Witt

On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence…

Classical Analysis and ODEs · Mathematics 2014-08-26 Rustum Choksi , Ihsan Topaloglu , Gantumur Tsogtgerel

Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives…

Optimization and Control · Mathematics 2023-02-01 C. Yalçın Kaya , Helmut Maurer

We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential…

Optimization and Control · Mathematics 2015-06-10 Hédy Attouch , Guillaume Garrigos

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of…

Optimization and Control · Mathematics 2011-07-18 Alberto Lovison

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Optimization and Control · Mathematics 2024-05-16 Didier Aussel , Parin Chaipunya

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise…

Machine Learning · Computer Science 2019-01-14 Ozan Sener , Vladlen Koltun

The article describes the proposition and application of a local search metaheuristic for multi-objective optimization problems. It is based on two main principles of heuristic search, intensification through variable neighborhoods, and…

Artificial Intelligence · Computer Science 2009-07-20 Martin Josef Geiger

In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…

Neural and Evolutionary Computing · Computer Science 2022-08-24 Liangli Zhen , Miqing Li , Ran Cheng , Dezhong Peng , Xin Yao