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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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 84; no. Suppl 2; pp. 1521 - 1553
Main Author: Nguyen Dinh, Tuan
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2021
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-021-09803-6