2006, 2nd ed., Universitext, ISBN 354035445X, 490

Data processing | Numerical analysis | Computer algorithms | Mathematical optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Mathematics | Operations Research, Mathematical Programming | Numerical and Computational Methods in Engineering | Algorithm Analysis and Problem Complexity

Book

Mathematical Programming, ISSN 0025-5610, 8/2018, Volume 170, Issue 2, pp. 569 - 570

We make corrections to the paper “Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations”, by M.S. Aronna, J.F....

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Control systems | Mathematical analysis | Optimal control | Wave equations | Mathematical programming

Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | Control systems | Mathematical analysis | Optimal control | Wave equations | Mathematical programming

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 2006, Volume 343, Issue 7, pp. 473 - 478

Dans cette Note, nous étudions un problème de commande optimale avec une commande scalaire et une contrainte sur l'état scalaire d'ordre quelconque. Les...

Journal Article

Applied Mathematics & Optimization, ISSN 0095-4616, 07/2019, pp. 1 - 34

An existence result for a class of mean field games of controls is provided. In the considered model, the cost functional to be minimized by each agent...

Existence theorems | Game theory | Games

Existence theorems | Game theory | Games

Journal Article

SIAM Journal on Financial Mathematics, ISSN 1945-497X, 2018, Volume 9, Issue 2, pp. 465 - 492

This paper performs a variational analysis for a class of European or American options with stochastic volatility models, including those of Heston and of...

Options | Parabolic variational inequalities | Partial differential equations | Finance | Variational formulation | BUSINESS, FINANCE | variational formulation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | REGULARITY | options | SOCIAL SCIENCES, MATHEMATICAL METHODS | partial differential equations | finance | parabolic variational inequalities | Mathematics | Optimization and Control

Options | Parabolic variational inequalities | Partial differential equations | Finance | Variational formulation | BUSINESS, FINANCE | variational formulation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | REGULARITY | options | SOCIAL SCIENCES, MATHEMATICAL METHODS | partial differential equations | finance | parabolic variational inequalities | Mathematics | Optimization and Control

Journal Article

2003, Universitext., ISBN 3540001913, xiii, 419

Book

Mathematical Programming, ISSN 0025-5610, 3/2018, Volume 168, Issue 1, pp. 717 - 757

In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the...

Wave equation | Partial differential equations | Heat equation | Theoretical, Mathematical and Computational Physics | 35L05 | 35K05 | Mathematics | Semigroup theory | 90C48 | Bilinear control systems | Mathematical Methods in Physics | 49K20 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Optimal control | Second-order optimality conditions | Combinatorics | Goh transform | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Blinear control systems | 2ND-ORDER ANALYSIS | Control systems | Differential equations | Operators (mathematics) | Nonlinear programming | Mathematical analysis | Optimization | Wave equations | Mathematics - Optimization and Control

Wave equation | Partial differential equations | Heat equation | Theoretical, Mathematical and Computational Physics | 35L05 | 35K05 | Mathematics | Semigroup theory | 90C48 | Bilinear control systems | Mathematical Methods in Physics | 49K20 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Optimal control | Second-order optimality conditions | Combinatorics | Goh transform | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Blinear control systems | 2ND-ORDER ANALYSIS | Control systems | Differential equations | Operators (mathematics) | Nonlinear programming | Mathematical analysis | Optimization | Wave equations | Mathematics - Optimization and Control

Journal Article

Systems & Control Letters, ISSN 0167-6911, 2012, Volume 61, Issue 1, pp. 143 - 147

We consider a linear quadratic stochastic optimal control problem with non-negativity control constraints. The latter are penalized with the classical...

Linear quadratic problems | Non-negativity control constraints | Stochastic control | Stochastic minimum principle | Logarithmic barrier | MAXIMUM PRINCIPLE | VARIANCE PORTFOLIO SELECTION | EQUATIONS | RANDOM-COEFFICIENTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINTS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Errors | Barriers | Optimal control | Control systems | Stochasticity | Estimates | Linear quadratic

Linear quadratic problems | Non-negativity control constraints | Stochastic control | Stochastic minimum principle | Logarithmic barrier | MAXIMUM PRINCIPLE | VARIANCE PORTFOLIO SELECTION | EQUATIONS | RANDOM-COEFFICIENTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSTRAINTS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | Errors | Barriers | Optimal control | Control systems | Stochasticity | Estimates | Linear quadratic

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2017, Volume 55, Issue 2, pp. 445 - 471

We propose some error estimates for the discrete solution of an optimal control problem with first-order state constraints, where the trajectories are...

Euler discretization | Rate of convergence | Nonlinear systems | Optimal control | State constraints | MATHEMATICS, APPLIED | 2ND-ORDER | rate of convergence | optimal control | PROGRAMMING-PROBLEMS | state constraints | nonlinear systems | 1ST | INEQUALITY CONSTRAINTS | OPTIMIZATION | DIFFERENCE APPROXIMATIONS | LIPSCHITZIAN STABILITY | Mathematics | Optimization and Control

Euler discretization | Rate of convergence | Nonlinear systems | Optimal control | State constraints | MATHEMATICS, APPLIED | 2ND-ORDER | rate of convergence | optimal control | PROGRAMMING-PROBLEMS | state constraints | nonlinear systems | 1ST | INEQUALITY CONSTRAINTS | OPTIMIZATION | DIFFERENCE APPROXIMATIONS | LIPSCHITZIAN STABILITY | Mathematics | Optimization and Control

Journal Article

10.
Second-order analysis of optimal control problems with control and initial-final state constraints

Journal of Convex Analysis, ISSN 0944-6532, 2010, Volume 17, Issue 3-4, pp. 885 - 913

This paper provides an analysis of Pontryagin minima satisfying a quadratic growth condition, for optimal control problems of ordinary differential equations...

MATHEMATICS | TANGENT SETS

MATHEMATICS | TANGENT SETS

Journal Article

11.
Full Text
Optimization of running strategies based on anaerobic energy and variations of velocity

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2014, Volume 74, Issue 5, pp. 1615 - 1636

The aim of this work is to present a model relying on a system of ordinary differential equations describing the evolution of the anaerobic energy and the...

Optimality conditions | Running race | Optimal control | Anaerobic energy | Singular arc | Energy recreation | State constraint | optimality conditions | singular arc | MATHEMATICS, APPLIED | state constraint | MATHEMATICAL-MODEL | anaerobic energy | RACE | CRITICAL POWER MODEL | running race | optimal control | energy recreation | Computer simulation | Dynamics | Mathematical analysis | Oscillations | Running | Strategy | Mathematical models | Optimization | Life Sciences | Biomechanics | Human health and pathology | Mechanics | Mathematics | Optimization and Control | Engineering Sciences | Physics | Tissues and Organs

Optimality conditions | Running race | Optimal control | Anaerobic energy | Singular arc | Energy recreation | State constraint | optimality conditions | singular arc | MATHEMATICS, APPLIED | state constraint | MATHEMATICAL-MODEL | anaerobic energy | RACE | CRITICAL POWER MODEL | running race | optimal control | energy recreation | Computer simulation | Dynamics | Mathematical analysis | Oscillations | Running | Strategy | Mathematical models | Optimization | Life Sciences | Biomechanics | Human health and pathology | Mechanics | Mathematics | Optimization and Control | Engineering Sciences | Physics | Tissues and Organs

Journal Article

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, ISSN 1492-8760, 2012, Volume 19, Issue 1-2, pp. 1 - 16

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 09/2014, Volume 29, Issue 5, pp. 964 - 978

This paper develops a theory of singular arc, and the corresponding second-order necessary and sufficient conditions, for the optimal control of a semilinear...

second-order optimality conditions | singular arc | optimal control | characterization of quadratic growth | parabolic equation | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMUM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STATE CONSTRAINTS | Economic models | Optimization | Mathematics | Optimization and Control

second-order optimality conditions | singular arc | optimal control | characterization of quadratic growth | parabolic equation | VARIATIONAL-INEQUALITIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MINIMUM | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STATE CONSTRAINTS | Economic models | Optimization | Mathematics | Optimization and Control

Journal Article

ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 08/2018

In this work we consider the time discretization of stochastic optimal control problems. Under general assumptions on the data, we prove the convergence of the...

Mathematics | Optimization and Control

Mathematics | Optimization and Control

Journal Article

Energy Systems, ISSN 1868-3967, 2/2018, Volume 9, Issue 1, pp. 59 - 77

We propose a novel method for the microgrid energy management problem by introducing a nonlinear, continuous-time, rolling horizon formulation. The method is...

Microgrid | Energy management system (EMS) | 90C39 | Optimization | Direct method | Engineering | Pontryagin Maximum Principle (PMP) | 49L20 | Energy Economics | Operations Research/Decision Theory | Optimal control | 93C15 | Energy Systems | Semi-Lagrangian scheme | 49J15 | Computer simulation | Switches | Linear programming | Maximum principle | Control systems | Electricity distribution | Integer programming | Mixed integer | Energy | Distributed generation | Mathematical models | Dynamic programming | Energy management | Mathematics

Microgrid | Energy management system (EMS) | 90C39 | Optimization | Direct method | Engineering | Pontryagin Maximum Principle (PMP) | 49L20 | Energy Economics | Operations Research/Decision Theory | Optimal control | 93C15 | Energy Systems | Semi-Lagrangian scheme | 49J15 | Computer simulation | Switches | Linear programming | Maximum principle | Control systems | Electricity distribution | Integer programming | Mixed integer | Energy | Distributed generation | Mathematical models | Dynamic programming | Energy management | Mathematics

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 8/2013, Volume 158, Issue 2, pp. 419 - 459

In this article, we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system...

Gauss–Newton method | Second order optimality condition | Mathematics | Theory of Computation | Stability analysis | Bang-singular control | Singular arc | Optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Shooting algorithm | Applications of Mathematics | Engineering, general | Gauss-Newton method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STATE | COMPUTATION | Algorithms | Studies | Control theory | Analysis | Jacobian matrix | Shooting | Mathematical analysis | Mathematical models | Derivatives | Shooting algorithms | Optimization and Control

Gauss–Newton method | Second order optimality condition | Mathematics | Theory of Computation | Stability analysis | Bang-singular control | Singular arc | Optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Optimal control | Shooting algorithm | Applications of Mathematics | Engineering, general | Gauss-Newton method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | STATE | COMPUTATION | Algorithms | Studies | Control theory | Analysis | Jacobian matrix | Shooting | Mathematical analysis | Mathematical models | Derivatives | Shooting algorithms | Optimization and Control

Journal Article

2006, ISBN 3540354476

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial...

Computer science | Operations research | Numerical analysis | Computer software | Mathematics | Mathematical optimization

Computer science | Operations research | Numerical analysis | Computer software | Mathematics | Mathematical optimization

Web Resource

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2013, Volume 159, Issue 1, pp. 1 - 40

This paper deals with optimal control problems of integral equations, with initial–final and running state constraints. The order of a running state constraint...

Calculus of Variations and Optimal Control; Optimization | Integral equations | Operations Research/Decision Theory | Optimal control | State constraints | Second-order optimality conditions | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMUM PRINCIPLE | REGULARITY | Studies | Optimization techniques | Lagrange multiplier | Control theory | Integrals | Lagrange multipliers | Dynamics | Quadratic forms | Running | Mathematics - Optimization and Control | Optimization and Control

Calculus of Variations and Optimal Control; Optimization | Integral equations | Operations Research/Decision Theory | Optimal control | State constraints | Second-order optimality conditions | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MAXIMUM PRINCIPLE | REGULARITY | Studies | Optimization techniques | Lagrange multiplier | Control theory | Integrals | Lagrange multipliers | Dynamics | Quadratic forms | Running | Mathematics - Optimization and Control | Optimization and Control

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2005, Volume 104, Issue 2, pp. 205 - 227

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming...

Mathematical Methods in Physics | Mathematics of Computing | Numerical Analysis | Mathematical and Computational Physics | Calculus of Variations and Optimal Control | Mathematics | Combinatorics | Optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED EQUATIONS | SETS | Studies | Nonlinear programming | Mathematical programming

Mathematical Methods in Physics | Mathematics of Computing | Numerical Analysis | Mathematical and Computational Physics | Calculus of Variations and Optimal Control | Mathematics | Combinatorics | Optimization | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GENERALIZED EQUATIONS | SETS | Studies | Nonlinear programming | Mathematical programming

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2014, Volume 366, Issue 4, pp. 2063 - 2087

In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints on the control. Our aim is to characterize...

Optimal control of PDE | Pontryagin's minimum principle | Strong minima | Second order optimality conditions | Control constraints | Local quadratic growth | control constraints | local quadratic growth | STATE CONSTRAINTS | ALGORITHM | PRINCIPLE | 2ND-ORDER ANALYSIS | CONSTRAINED CONTROL-PROBLEMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | SYSTEMS | strong minima | second order optimality conditions

Optimal control of PDE | Pontryagin's minimum principle | Strong minima | Second order optimality conditions | Control constraints | Local quadratic growth | control constraints | local quadratic growth | STATE CONSTRAINTS | ALGORITHM | PRINCIPLE | 2ND-ORDER ANALYSIS | CONSTRAINED CONTROL-PROBLEMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | SYSTEMS | strong minima | second order optimality conditions

Journal Article

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