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In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…

Optimization and Control · Mathematics 2021-07-28 Soufiane Yahyaoui , Lahoussine Lafhim , Mohamed Ouzahra

In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna , Frédéric Bonnans , Bean San Goh

We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary…

Optimization and Control · Mathematics 2015-11-24 Simao P. S. Santos , Natalia Martins , Delfim F. M. Torres

In this paper we present a finite element analysis for a Dirichlet boundary control problem governed by the Stokes equation. The Dirichlet control is considered in a convex closed subset of the energy space $\mathbf{H}^1(\Omega).$ Most of…

Numerical Analysis · Mathematics 2021-11-01 Thirupathi Gudi , Ramesh Ch. Sau

This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in mathematical programming, including…

Optimization and Control · Mathematics 2026-04-29 M. Benko , H. Gfrerer , J. J. Ye , J. Zhang , J. Zhou

We consider semilinear parabolic optimal control problems subject to Neumann boundary conditions, control constraints, and an infinite time horizon. The control constraints are pointwise in time, but they can be pointwise or integral in the…

Optimization and Control · Mathematics 2026-03-20 Eduardo Casas , Nicolai Jork

A scheme for generating a family of convex variational principles is developed, the Euler- Lagrange equations of each member of the family formally corresponding to the necessary conditions of optimal control of a given system of ordinary…

Optimization and Control · Mathematics 2025-06-13 Amit Acharya , Janusz Ginster

This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…

Optimization and Control · Mathematics 2025-07-18 Xiaoxiao Ma , Wei Ouyang , Jane Ye , Binbin Zhang

We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin's Maximum Principle type.…

Optimization and Control · Mathematics 2016-10-31 Chems Eddine Arroud , Giovanni Colombo

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

Optimization and Control · Mathematics 2016-06-09 Xiaojing Zhang , Maryam Kamgarpour , Angelos Georghiou , Paul Goulart , John Lygeros

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…

Optimization and Control · Mathematics 2019-04-26 Salvatore Federico , Giorgio Ferrari , Frank Riedel , Michael Röckner

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2015-06-09 Ugur G. Abdulla

In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…

Optimization and Control · Mathematics 2018-10-03 Xu Liu , Qi Lü , Xu Zhang

We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary…

Optimization and Control · Mathematics 2015-06-22 Simao P. S. Santos , Natalia Martins , Delfim F. M. Torres

This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex.…

Probability · Mathematics 2017-07-27 Qingxin Meng , Qiuhong Shi , Maoning Tang

This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…

Optimization and Control · Mathematics 2021-11-01 Ashkan Mohammadi , Boris Mordukhovich

In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation…

Optimization and Control · Mathematics 2024-08-21 Xiaojuan Li , Mingshang Hu

We analyze, in two dimensions, an optimal control problem for the Navier--Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular…

Optimization and Control · Mathematics 2022-08-19 Francisco Fuica , Felipe Lepe , Enrique Otarola , Daniel Quero

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…

Optimization and Control · Mathematics 2017-02-08 Leonardo Colombo