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Carathéodory-John–type sufficiency criteria in continuous-time nonlinear programming under generalized $$(\alpha,\rho)-(\eta,\theta)-$$type I invexity. (English) Zbl 1289.90205
Summary: We introduce the class of $$(\alpha,\rho)-(\eta,\theta)-$$pesudo strictly pseudo-type I invexity functions. We establish Carathéodory-John–type sufficient optimality conditions for a continuous-time nonlinear programming problem with nonlinear operator equality and inequality constraints under generalized $$(\alpha,\rho)-(\eta,\theta)-$$type I invexity conditions.

##### MSC:
 90C30 Nonlinear programming 90C46 Optimality conditions and duality in mathematical programming 90C48 Programming in abstract spaces