Nonsmooth Continuous-time Multiobjective Optimization Problems |
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A.M. Moya Algebra arguments assertion assume assumptions Banach space basic Clarke regular Class closed convex subsets concept conclude conditions of optimality constraint qualification continuous continuous-time contradicts Corollary denoted Derivatives directional derivative E-mail Elliptic Equation exist µ Extensor fact Fields Figueiredo fj(t follows function defined g₁(t Geometric gi(t given gradient grant Hence inequality integrable interim hypothesis inver invex at I(t least Lebesgue measurable Lemma locally Lipschitz M.A. Rojas-Medar Metric mono-objective multifunction Multiobjective Optimization multiplier nonempty nonsmooth nonzero norm objective obtain Øj(x positive problem VCNP PROOF properly efficient solution prove qualification 12 Removal respect Rocha Rodrigues Jr Santos satisfying similar solution of VCNP space Spain strict strictly invex sufficient conditions Suppose further Theorem 3.3 throughout 0.T Universidade usual weak efficient solution Σ µ