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Second-order optimality conditions for nonlinear programs and mathematical programs
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 (O...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2017
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5591379/ https://www.ncbi.nlm.nih.gov/pubmed/28955151 http://dx.doi.org/10.1186/s13660-017-1487-8 |
Sumario: | 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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