Optimality Conditions for Distributed Control Problems with Nonlinear State Equation

DOI10.1137/0323008zbMath0561.49017OpenAlexW1983700811MaRDI QIDQ5186241

Dan Tiba

Publication date: 1985

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0323008

zbMATH Keywords

nonlinear abstract evolution equationsconvex cost functionals

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational inequalities (49J40) Control/observation systems governed by partial differential equations (93C20) Monotone operators and generalizations (47H05) Nonlinear parabolic equations (35K55) Equations involving nonlinear operators (general) (47J05) Nonlinear systems in control theory (93C10) Partial functional-differential equations (35R10) First-order nonlinear hyperbolic equations (35L60) Control/observation systems in abstract spaces (93C25) Optimality conditions for problems in abstract spaces (49K27)

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A variational inequality approach to constrained control problems for parabolic equations ⋮ On the control of strongly nonlinear hyperbolic systems ⋮ Optimal control of nonlinear evolution systems in the case where the solution is not differentiable with respect to the control ⋮ Analysis and semidiscrete Galerkin approximation of a class of nonlinear parabolic optimal control problems ⋮ Optimal control of quasilinear parabolic equations ⋮ Second order optimality conditions for optimal control of quasilinear parabolic equations ⋮ New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations ⋮ Optimal control of parabolic variational inequalities with state constraint ⋮ The optimality principle for discrete and first order partial differential inclusions ⋮ Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem ⋮ Optimal control of hyperbolic \(H\)-hemivariational inequalities with state constraints

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