Second-order necessary optimality conditions for an optimal control problem with nonlinear state equations
type: Item
instance of: scholarly article
title: Second-order necessary optimality conditions for an optimal control problem with nonlinear state equations
zbMATH Open document ID: 1485.49009
author: Nguyen Thi Toan
author: Le Quang Thuy
published in: Positivity
publication date: 2022-03-15T00:00:00Z
review text: Second-order necessary optimality conditions are derived for an optimal control problem (OCP) with nonconvex cost function, nonlinear state equation and mixed constraints using tools from functional analysis. An example is given showing that if the second-order necessary condition is not satisfied, then the admissible couple is not a solution even it satisfies first-order necessary conditions.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49J21
Mathematics Subject Classification ID: 49K21
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 7490114
zbMATH Keywords: first-order optimality condition
zbMATH Keywords: second-order optimality condition
zbMATH Keywords: optimal control problem
zbMATH Keywords: nonlinear state equation
zbMATH Keywords: mixed constraint
reviewed by: Bülent Karasözen
MaRDI profile type: Publication
full work available at URL: s11117-022-00898-x
OpenAlex ID: W4212818424
cites work: Second-order and related extremality conditions in nonlinear programming
cites work: Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
cites work: First- and second-order optimality conditions for optimal control problems of state constrained integral equations
cites work: Q4503250
cites work: Sufficient Second-Order Optimality Conditions for Semilinear Control Problems with Pointwise State Constraints
cites work: A Connection Between the Maximum Principle and Dynamic Programming for Constrained Control Problems
cites work: Q4743352
cites work: Further results on subgradients of the value function to a parametric optimal control problem
cites work: Metric regularity, tangent sets, and second-order optimality conditions
cites work: Perturbations, approximations and sensitivity analysis of optimal control systems
cites work: Pointwise second-order necessary optimality conditions for the Mayer problem with control constraints
cites work: Q5261771
cites work: Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variational Inequalities
cites work: Second Order Sufficiency Criteria for a Discrete Optimal Control Problem
cites work: Discrete Optimal Control: Second Order Optimality Conditions
cites work: Variational approach to second-order optimality conditions for control problems with pure state constraints
cites work: Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality
cites work: Q4194725
cites work: An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems
cites work: Second-Order Necessary Optimality Conditions for a Class of Semilinear Elliptic Optimal Control Problems with Mixed Pointwise Constraints
cites work: Second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints
cites work: Lower Semicontinuity of the Solution Set to a Parametric Optimal Control Problem
cites work: Second order sufficient optimality conditions for hybrid control problems with state jump
cites work: Second-order sufficient conditions for state-constrained optimal control problems
cites work: Lipschitz Continuity of Solutions of Linear Inequalities, Programs and Complementarity Problems
cites work: Optimality conditions for discrete optimal control problems
cites work: Optimality conditions for discrete optimal control problems with equality and inequality type of constraints
cites work: Second-order optimality conditions in a discrete optimal control problem
cites work: Epsilon-Maximum Principle of Pontryagin Type and Perturbation Analysis of Convex Optimal Control Problems
cites work: Nonsmooth Optimum Problems with Constraints
cites work: Optimum Problems with Certain Lower Semicontinuous Set-Valued Constraints
cites work: Characterization of \(L^1\)-closed decomposable sets in \(L^\infty\)
cites work: Optimal Control Problems with Set-Valued Control and State Constraints
cites work: Optimality conditions in mathematical programming and composite optimization
cites work: Variational Analysis
cites work: Convexity in Hamilton--Jacobi theory. I: Dynamics and duality
cites work: Convexity in Hamilton--Jacobi theory. II: Envelope representations
cites work: Subgradients of the value function to a parametric optimal control problem
cites work: Mordukhovich subgradients of the value function in a parametric optimal control problem
cites work: Second-order necessary optimality conditions for a discrete optimal control problem
cites work: Second-order necessary optimality conditions for a discrete optimal control problem with mixed constraints
cites work: Second-order necessary optimality conditions for an optimal control problem
cites work: Second-order KKT optimality conditions for multiobjective discrete optimal control problems
DOI: 10.1007/S11117-022-00898-X
description: scientific article; zbMATH DE number 7490114