Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Invex functions and generalized convexity in multiobjective programming
Journal of Optimization Theory and Applications
Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces
Journal of Optimization Theory and Applications
The Euler approximation in state constrained optimal control
Mathematics of Computation
Multi-objective infinite programming
Computers & Mathematics with Applications
On G-invex multiobjective programming. Part I. Optimality
Journal of Global Optimization
On G-invex multiobjective programming. Part II. Duality
Journal of Global Optimization
Brief paper: Optimal switching instants for a switched-capacitor DC/DC power converter
Automatica (Journal of IFAC)
Nonsmooth multiobjective continuous-time problems with generalized invexity
Journal of Global Optimization
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Second-order Kuhn-Tucker invex constrained problems
Journal of Global Optimization
Nonsmooth semi-infinite programming problem using Limiting subdifferentials
Journal of Global Optimization
Duality for optimization problems in Banach algebras
Journal of Global Optimization
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This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented.