Generalized B-vex functions and generalized B-vex programming. (English) Zbl 0802.49027

Summary: A class of functions called pseudo \(B\)-vex and quasi \(B\)-vex functions is introduced by relaxing the definitions of \(B\)-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of \(B\)-invex, pseudo \(B\)- invex, and quasi \(B\)-invex functions is defined as a generalization of \(B\)-vex, pseudo \(B\)-vex, and quasi \(B\)-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving \(B\)-vex and \(B\)-invex functions.


49M37 Numerical methods based on nonlinear programming
49J52 Nonsmooth analysis
49K27 Optimality conditions for problems in abstract spaces
Full Text: DOI


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