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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

Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…

Optimization and Control · Mathematics 2016-06-20 M. Hassan Farshbaf-Shaker , Christian Heinemann

In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We…

Optimization and Control · Mathematics 2022-12-26 Jianjun Zhou

In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding…

Optimization and Control · Mathematics 2018-03-15 Gianni Gilardi , Jürgen Sprekels

This paper focuses on optimality conditions for $C^{1,1}$-smooth optimization problems subject to inequality and equality constraints. By employing the concept of limiting (Mordukhovich) second-order subdifferentials to the Lagrangian…

Optimization and Control · Mathematics 2024-12-30 Duong Thi Viet An , Nguyen Van Tuyen

In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…

Optimization and Control · Mathematics 2013-02-15 Loïc Bourdin , Emmanuel Trélat

Over the last years, minimization problems over spaces of measures have received increased interest due to their relevance in the context of inverse problems, optimal control and machine learning. A fundamental role in their numerical…

Optimization and Control · Mathematics 2024-03-19 Gerd Wachsmuth , Daniel Walter

This work investigates the well-posedness and optimal control of a sixth-order Cahn-Hilliard equation, a higher-order variant of the celebrated and well-established Cahn-Hilliard equation. The equation is endowed with a source term, where…

Analysis of PDEs · Mathematics 2024-05-01 Pierluigi Colli , Gianni Gilardi , Andrea Signori , Jürgen Sprekels

In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint…

Optimization and Control · Mathematics 2019-05-14 Yi-Bin Xiao , Nguyen Van Tuyen , Ching-Feng Wen , Jen-Chih Yao

We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.

Optimization and Control · Mathematics 2022-08-26 Gerd Wachsmuth

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

The mathematical modeling of numerous real-world applications results in hierarchical optimization problems with two decision makers where at least one of them has to solve an optimal control problem of ordinary or partial differential…

Optimization and Control · Mathematics 2019-06-20 Patrick Mehlitz , Gerd Wachsmuth

The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations,…

Optimization and Control · Mathematics 2023-02-14 Yassine Tahraoui , Fernanda Cipriano

This paper addresses an optimal control problem governed by a rate independent evolution involving an integral operator. Its particular feature is that the dissipation potential depends on the history of the state. Because of the non-smooth…

Optimization and Control · Mathematics 2023-12-19 Livia Betz

We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…

Optimization and Control · Mathematics 2019-12-19 Yves Achdou , Mathieu Laurière , Pierre-Louis Lions

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

Analysis of PDEs · Mathematics 2017-09-08 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-Cahn equation using distributed controls that satisfy…

Numerical Analysis · Mathematics 2022-07-27 Konstantinos Chrysafinos , Dimitra Plaka

We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…

Optimization and Control · Mathematics 2021-12-03 Masoumeh Hashemi , Roland Herzog , Thomas M. Surowiec

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 formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…

Optimization and Control · Mathematics 2026-04-16 Enrico Sartor