Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
Nonlinear Uncertain Systems and Necessary Conditions of Optimality
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pontryagin's principle for time-optimal problems
Journal of Optimization Theory and Applications
Convex analysis and variational problems
Convex analysis and variational problems
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In this paper we study nonlinear parametric optimal control problems. We formulate the relevant minimax problem and prove the existence of an optimal control. Also we derive necessary conditions for saddle point optimality. We also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem. Finally we present two examples of parabolic distributed parameter systems, which illustrate the abstract results.