## Convex analysis and optimization |

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A.D. Ioffe absolute additive Borel absolute Borel class absolute multiplicative Borel additive Borel class additive class admissible pair applications assumption Aubin Banach space Borel set C.A. Rogers calculus of variations Clarke closed sets constraint control problem convex analysis convex set countable curves defined denote derivative differential equations dual problem duality Ekeland equivalent exists f is differentiable f is l.s.c. f maps F set f(xQ function f function on Sn gradient Hiriart-Urruty homeomorphism infimal convolution Ioffe's J.E. Jayne Kutateladze Lemma Let f linear operators Lipschitzian locally Lipschitz Math mathematical Maximum Principle metric space multiplicative Borel class multiplicative class nonsmooth analysis Nowosad open sets optimal control proper convex function proper map properties Proposition prove quasiconvex functions result Rockafellar satisfying sequence set-valued map strict prederivative subdifferential subset support function theory vector