## Nonsmooth continuous-time multiobjective optimization problems |

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a.e. t G A.M. Moya Banach space Batista dos Santos Clarke generalized directional Clarke regular closed convex subsets conditions of optimality constraint qualification 12 Continuous-Time Multiobjective Optimization contradicts Corollary Covariant Derivatives denoted directional derivative Elliptic Equation exist JL exist x G F Extensor Fields Fernandez and W.A. fj(t Fritz-John function defined Furtado G J respectively Geometric Algebra gi(t gradient grangean Hence integrably bounded Integration of Multifunctions interim hypothesis invex at x(t invexity hypothesis L. X. Figueiredo Lagrangean function limsup Luiz A. B. San M.A. Rojas-Medar Marcelo F measurable functions mono-objective Multivector and Extensor nonempty subset nonsmooth nonzero normed space Oj(x Osuna-Gomez partially supported pj(x problem VCNP properly efficient solution regular and invex Rocha Rodnques Jr Semigroups solution of problem solution of VCNP strictly invex sufficient conditions support functions Suppose further Theorem 3.3 throughout O.T unit ball V.V. Fernandez V7 G J W.A. Rodriques Jr weak efficient solution