摘要 : We analyze the optimal value function v associated with a general parametric optimization problem via the theory of viscosity solutions. The novelty is that we obtain regularity properties of v by showing that it is a viscosity so... 展开 We analyze the optimal value function v associated with a general parametric optimization problem via the theory of viscosity solutions. The novelty is that we obtain regularity properties of v by showing that it is a viscosity solution to a set of first-order equations. As a consequence, in Banach spaces, we provide sufficient conditions for local and global Lipschitz properties of v. We also derive, in finite dimensions, conditions for optimality through a comparison principle. Finally, we study the relationship between viscosity and Clarke generalized solutions to get further differentiability properties of v in Euclidean spaces. (c) 2021 Elsevier Inc. All rights reserved. 收起