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Second-order optimality conditions for nonlinear programs and mathematical programs
1Department of Mathematics, Faculté des Sciences et Techniques, University Cadi Ayyad, B.P. 549, Marrakech, Morocco.
Abstract:
It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order γ with the help of first- and second-order approximations derived from (Optimization 40(3):229-246, 2011) and we study their characterization. Further, we give an example of such a function that arises quite naturally in nonlinear analysis and optimization. An extension of Newton's method is also given and proved to solve Euler equation with second-order approximation data.
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