Optimization and Nonsmooth Analysis |
Contents
Introduction and Preview | 1 |
Generalized Gradients | 24 |
Differential Inclusions | 110 |
Copyright | |
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af(x assertion Banach space belongs Bolza bounded C₁ calculus of variations Chapter Clarke classical compact completes the proof cone constant constraints converging convex analysis convex cone convex function convex hull convex set Corollary dc(x deduce defined definition denote derive DF(x directionally Lipschitz element epi ƒ equation example exists F is Lipschitz f₁ finite follows function f ƒ is regular given gradient Hamilton-Jacobi equation Hamiltonian hypertangent hypotheses implies inequality int Tc(x Lemma Let f lim sup Lipschitz condition locally Lipschitz lower semicontinuous mapping maximum principle minimizing multifunction Nc(x necessary conditions neighborhood nonempty nonnegative nonsmooth normal Note optimal control Proposition Let result Rockafellar s₁ satisfies Section sequence solution solves subset suffices to prove sufficiently suppose Theorem Let theory trajectory upper semicontinuous v₁ vector x₁ µ(ds µ(dt