2015/08/27 by Dmitry Khlopin, Khlopin, Dmitry
Computer Science · Mathematics · #49J52 #49K15 #49K40 #49L20 #91B62 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1508.06777
openalex publication_date 2015/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the normal form version of the Pontryagin Maximum Principle is a necessary and sufficient condition for the optimality criteria that correspond to this value function. Different criteria of optimality under different asymptotic constraints may be used, including almost strong and classical optimality proposed by D.Bogusz. Special attention is devoted to weakly agreeable criteria. We also obtain the conditions on control system (like controllability) that guarantee the Lipschitz continuity of the value function, without any other asymptotic conditions besides finiteness of the value function. Some examples are discussed. In particular, it was shown that the same control, regarded as agreeable optimal and overtaking optimal control, can correspond to different (everywhere) value functions.