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Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

Optimization and Control · Mathematics 2021-12-14 Eduardo Casas , Karl Kunisch

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

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…

Optimization and Control · Mathematics 2024-10-01 Cung The Anh , Nguyen Hai Ha Giang

We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…

Optimization and Control · Mathematics 2013-01-30 M. Barbero-Liñán , B. Jakubczyk

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…

Optimization and Control · Mathematics 2008-12-20 Seid Bahlali

A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality…

Optimization and Control · Mathematics 2023-09-06 Huynh Khanh , Bui Trong Kien

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with…

Optimization and Control · Mathematics 2013-10-17 J. Frédéric Bonnans , Constanza De La Vega , Xavier Dupuis

In this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two dimensional bounded domain. The distributed optimal control problem is framed as the…

Optimization and Control · Mathematics 2018-09-28 Tania Biswas , Sheetal Dharmatti , Manil T Mohan

The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…

Optimization and Control · Mathematics 2019-01-23 Hélène Frankowska , Qi Lü

A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove…

Optimization and Control · Mathematics 2024-02-06 Huynh Khanh , Bui Trong Kien

We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions,…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels

PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…

Numerical Analysis · Mathematics 2016-11-23 Margherita Porcelli , Valeria Simoncini , Martin Stoll

This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…

Optimization and Control · Mathematics 2026-04-24 Eduardo Casas , Karl Kunisch

In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type govern the evolution of coupled diffuse phase transition…

Optimization and Control · Mathematics 2023-03-30 Jürgen Sprekels , Fredi Tröltzsch

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…

Optimization and Control · Mathematics 2019-03-15 Nguyen Huy Chieu , Le Van Hien , Tran T. A. Nghia , Ha Anh Tuan

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…

Optimization and Control · Mathematics 2015-03-25 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a…

Optimization and Control · Mathematics 2025-06-25 Casas Eduardo , Mateos Mariano

In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…

Optimization and Control · Mathematics 2025-02-14 Li Deng

In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna , Frédéric Bonnans , Axel Kröner