Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints

We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach space, and with final-state constraints, pointwise pure state constraints and a mixed pointwise control-state constraint. Basing on necessary opti...

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Vydáno v:	Applied mathematics & optimization Ročník 84; číslo Suppl 2; s. 1521 - 1553
Hlavní autor:	Nguyen Dinh, Tuan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.12.2021 Springer Nature B.V
Témata:	Banach spaces Calculus of Variations and Optimal Control; Optimization Continuity (mathematics) Control Lagrange multiplier Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Multiple objective analysis Numerical and Computational Physics Operators (mathematics) Optimal control Original Paper Pareto optimization Quadratic forms Simulation Systems Theory Theoretical Banach space-valued integration 49K20 90C46 Multiobjective optimal control Necessary second-order optimality condition 90C29 Bilinear control system Semigroup structure 35J25 49K27 Local weak Pareto solution
ISSN:	0095-4616, 1432-0606
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Abstract	We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach space, and with final-state constraints, pointwise pure state constraints and a mixed pointwise control-state constraint. Basing on necessary optimality conditions obtained for an abstract multiobjective optimization framework, we establish a second-order Lagrange multiplier rule, of Fritz-John type, for local weak Pareto solutions of the problem under study. As a consequence of the main result, we also derive a multiplier rule for a multiobjective optimal control model driven by a bilinear system being affine-linear in the control, and with an objective function of continuous quadratic form.
AbstractList	We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach space, and with final-state constraints, pointwise pure state constraints and a mixed pointwise control-state constraint. Basing on necessary optimality conditions obtained for an abstract multiobjective optimization framework, we establish a second-order Lagrange multiplier rule, of Fritz-John type, for local weak Pareto solutions of the problem under study. As a consequence of the main result, we also derive a multiplier rule for a multiobjective optimal control model driven by a bilinear system being affine-linear in the control, and with an objective function of continuous quadratic form.
Author	Nguyen Dinh, Tuan
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CitedBy_id	crossref_primary_10_1007_s10957_022_02143_7 crossref_primary_10_1016_j_jmaa_2023_127024
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Keywords	Banach space-valued integration 49K20 90C46 Multiobjective optimal control Necessary second-order optimality condition 90C29 Bilinear control system Semigroup structure 35J25 49K27 Local weak Pareto solution
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Snippet	We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach...
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SubjectTerms	Banach spaces Calculus of Variations and Optimal Control; Optimization Continuity (mathematics) Control Lagrange multiplier Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Multiple objective analysis Numerical and Computational Physics Operators (mathematics) Optimal control Original Paper Pareto optimization Quadratic forms Simulation Systems Theory Theoretical
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Title	Second-Order Lagrange Multiplier Rules in Multiobjective Optimal Control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints
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