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Advances in Pure and Applied Mathematics, ISSN 1867-1152, 10/2019, Volume 10, Issue 4, pp. 437 - 446
We prove some important properties of the -resolvent mapping recently introduced by B. J. Choi and U. C. Ji, The proximal point algorithm in uniformly convex... 
47H09 | 47H10 | 49J20 | fixed point | 49J40 | proximal point algorithm
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 12/2018, Volume 43, Issue 12, pp. 1761 - 1802
We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in... 
optimality conditions | 35Q91 | 49K20 | Congestion game | 49J20 | optimal transport | minimal action curves | regularity | Moser iteration
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 11/2019, Volume 40, Issue 15, pp. 1721 - 1767
We analyze the Ericksen-Leslie system equipped with the Oseen-Frank energy in three space dimensions. Recently, the author introduced the concept of... 
49J20 | 35A35 | 35Q35 | 76A15 | Ericksen-Leslie | optimal control | Dissipative solutions | liquid crystal | numerical approximation | Energy dissipation | Optimal control | Approximation
Journal Article
International Journal of Control, ISSN 0020-7179, 11/2019, Volume 92, Issue 11, pp. 2693 - 2700
The aim of this paper is to control an electromagnetic wave that penetrates in a medium with some missing information about its physical properties. The... 
electromagnetic waves | averaged control | 49J20 | Optimal control | missing data problems | no-regret control | 93C20 | 93C41 | DISTRIBUTED SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Missing data | Wave propagation | Propagation velocity | Electromagnetic radiation | Dirichlet problem | Physical properties | Optimization
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2016, Volume 55, Issue 6, pp. 1 - 44
We present a way to study a wide class of optimal design problems with a perimeter penalization. More precisely, we address existence and regularity properties... 
49J35 | 49N60 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Primary 49J20 | 49Q20 | Secondary 49J45 | MATHEMATICS | MATHEMATICS, APPLIED | RELAXATION | BOUNDARY | OPTIMAL-DESIGN PROBLEM | QUASICONVEXITY
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 2/2018, Volume 25, Issue 1, pp. 1 - 26
We introduce the notion of stable solution in mean field game theory: they are locally isolated solutions of the mean field game system. We prove that such... 
35Q91 | Mathematics | 49J20 | 49L25 | Analysis | MATHEMATICS, APPLIED | FICTITIOUS PLAY | Computer entertainment systems | Game theory | Optimization and Control
Journal Article
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, ISSN 0944-2669, 10/2019, Volume 58, Issue 5, p. 1
This paper is devoted to the analysis of problems of optimal control of ensembles governed by the Liouville (or continuity) equation. The formulation and study... 
MATHEMATICS | MATHEMATICS, APPLIED | COST | 49K20 | Secondary 35L03 | 35B65 | EQUATIONS | Primary 49J20 | 35Q93 | Analysis | Cost control | Investigations | Analysis of PDEs | Mathematics | Optimization and Control
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 12/2013, Volume 2, Issue 4, pp. 427 - 433
In this paper we investigate a maximax optimization problem related to a homogeneous Dirichlet problem in two classes of rearrangements. We prove existence and... 
35J20 | Mathematics, general | Mathematics | 49J20
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2017, Volume 56, Issue 6, pp. 1 - 40
We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how... 
49J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 74B10
Journal Article
Tatra Mountains Mathematical Publications, ISSN 1210-3195, 12/2018, Volume 71, Issue 1, pp. 9 - 25
We consider a control problem for one-dimensional heat equation with quadratic cost functional. We prove the existence and uniqueness of a control function... 
quadratic cost functional | 35K20 | heat equation | 49J20 | 35Q79 | exact controllability | extremal problem | dense controllability | 35Q93
Journal Article
Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 33
In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion... 
Variational inclusion problem | Maximal monotone mapping | Convex minimization problem | Mathematics | Resolvent operators | Viscosity iterative method | 47H10 | 49J20 | Analysis | 49J40 | 47H09 | Mathematics, general | Strictly pseudocontractions | Applications of Mathematics
Journal Article
Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 13
In this paper, we investigate a variational discretization approximation of parabolic bilinear optimal control problems with control constraints. For the state... 
49J20 | Variational discretization | Analysis | Mathematics, general | Mathematics | 65M60 | Superconvergence | Applications of Mathematics | Bilinear optimal control | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | FINITE-ELEMENT METHODS
Journal Article
International Journal of Control, ISSN 0020-7179, 11/2017, Volume 90, Issue 11, pp. 2349 - 2367
Fast first-order proximal methods that solve linear and bilinear parabolic optimal control problems with a sparsity cost functional are discussed. Weak... 
semi-smooth Newton method | Optimal control theory | proximal method | 49K20 | 49J20 | non-smooth optimisation | 49J52 | parabolic PDE | 49N05 | 35K10 | SPACES | SIGNAL RECOVERY | ALGORITHM | EQUATIONS | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | Control theory | Sparsity | Functionals | Optimal control
Journal Article
Arabian Journal of Mathematics, ISSN 2193-5343, 3/2015, Volume 4, Issue 1, pp. 41 - 58
We consider the problem to control a vibrating string to rest in a given finite time. The string is fixed at one end and controlled by Neumann boundary control... 
35L05 | Mathematics, general | Mathematics | 49J20 | 93C20
Journal Article
Tatra Mountains Mathematical Publications, ISSN 1210-3195, 12/2018, Volume 71, Issue 1, pp. 27 - 37
We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a simply... 
35L85 | 74K20 | 49J20 | Vibrating viscoelastic plate | 49J40 | optimal control | 74D10 | rigid obstacle | variable thickness
Journal Article
Mathematics of Operations Research, ISSN 0364-765X, 08/2019
Uncertainty pervades virtually every branch of science and engineering, and in many disciplines, the underlying phenomena can be modeled by partial... 
MATHEMATICS AND COMPUTING
Journal Article
International Journal of Control, ISSN 0020-7179, 10/2015, Volume 88, Issue 10, pp. 2117 - 2125
In this paper, we deal with the optimal control problem governed by multidimensional modified Swift-Hohenberg equation. After showing the relationship between... 
optimal control | modified Swift-Hohenberg equation | 49J20 | 35K57 | 49J30 | optimality condition | SYSTEM | INSTABILITY | CAHN-HILLIARD EQUATION | MODEL | AUTOMATION & CONTROL SYSTEMS | Optimization | Approximation | Mathematical analysis | Optimal control
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2019, Volume 58, Issue 5, pp. 1 - 34
This paper is devoted to the analysis of problems of optimal control of ensembles governed by the Liouville (or continuity) equation. The formulation and study... 
49K20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Secondary 35L03 | Analysis | Theoretical, Mathematical and Computational Physics | 35B65 | Mathematics | Primary 49J20 | 35Q93
Journal Article
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