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Related papers: Second-order analysis for the time crisis problem

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In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…

Optimization and Control · Mathematics 2017-12-29 Bui Trong Kien , Nguyen Van Tuyen , Jen-Chih Yao

The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…

Optimization and Control · Mathematics 2024-11-07 Cyrille Kenne , Landry Djomegne , Pascal Zongo

We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…

Optimization and Control · Mathematics 2026-03-30 Stefano Bosi , David Desmarchelier , Ngoc-Sang Pham

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…

Optimization and Control · Mathematics 2013-11-01 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…

Optimization and Control · Mathematics 2023-05-10 Moisés Rodrigues Cirilo do Monte , Valeriano Antunes de Oliveira

In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…

Optimization and Control · Mathematics 2020-02-13 Eduardo Casas , Daniel Wachsmuth

In this paper we study the optimal control of an initial-boundary value problem for the classical nonviscous Cahn-Hilliard system with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive…

Optimization and Control · Mathematics 2024-06-12 Pierluigi Colli , Jürgen Sprekels

An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…

Optimization and Control · Mathematics 2017-03-28 Hongwei Lou , Jiongmin Yong

We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…

Optimization and Control · Mathematics 2024-03-04 Eduardo Casas , Mariano Mateos , Arnd Rösch

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

Optimization and Control · Mathematics 2021-07-09 Laurent Pfeiffer , Xiaolu Tan , Yulong Zhou

In this paper we study second-order optimality conditions for non-convex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well-known that second-order optimality conditions involve the support…

Optimization and Control · Mathematics 2020-01-15 Helmut Gfrerer , Jane Ye , Jinchuan Zhou

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…

Optimization and Control · Mathematics 2011-10-21 B. S. Mordukhovich , R. T. Rockafellar

In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…

Optimization and Control · Mathematics 2022-05-18 Eduardo Casas , Mariano Mateos

For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…

Optimization and Control · Mathematics 2024-05-24 Karl Kunisch , Fredi Troeltzsch

An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…

Optimization and Control · Mathematics 2015-07-01 Nikolay Pogodaev

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

The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimization problem, and then the necessary optimality conditions…

Optimization and Control · Mathematics 2023-10-06 Denis Khimin , Johannes Lankeit , Marc C. Steinbach , Thomas Wick

In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description…

Quantum Physics · Physics 2015-10-27 Francesca Albertini , Domenico D'Alessandro

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

This paper on the whole concerns with the duality of Mayer problem for k-th order differential inclusions, where k is an arbitrary natural number. Thus, this work for constructing the dual problems to differential inclusions of any order…

Optimization and Control · Mathematics 2019-06-20 Elimhan N. Mahmudov