## Methods of Dynamic and Nonsmooth OptimizationPresents the elements of a unified approach to optimization based on 'nonsmooth analysis', a term introduced in the 1970's by the author, who is a pioneer in the field. Based on a series of lectures given at a conference at Emory University in 1986, this volume presents its subjects in a self-contained and accessible manner. The topics treated here have been in an active state of development. Focuses mainly on deterministic optimal control, the calculus of variations, and mathematical programming. In addition, it features a tutorial in nonsmooth analysis and geometry and demonstrates that the method of value function analysis via proximal normals is a powerful tool in the study of necessary conditions, sufficient conditions, controllability, and sensitivity analysis. The distinction between inductive and deductive methods, the use of Hamiltonians, the verification technique, and penalization are also emphasized. |

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ac(t apply arc p satisfying boundary conditions calculus of variations Chapter classical coercive consider constant context converge convex convex function deduce defined definition denote differential inclusion problem directional derivatives dual action dynamic programming endpoint constraints equivalent Euler equation Euler inclusion everywhere example Existence Theorem extended extended-valued finite formula function f given growth condition Hamilton–Jacobi equation Hamiltonian inclusion hypotheses implies inequality infimum infinite-dimensional integral isoperimetric problem Lagrangian Lipschitz functions Lipschitz rank locally Lipschitz lower semicontinuous maximum principle method minimize necessary conditions non-Lipschitz nonempty nonsmooth analysis Note optimal control optimal control problem parameter perturbed proof properties Proposition 3.1 prove proximal normal proximal subgradient result role ſ L(t sequence smooth solves standard variational argument subdifferential subgradients suppose Theorem 2.1 theory tion Tonelli's Existence Theorem trajectory transversality condition value function variable vector verification function