Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives

Felipe Lara ()
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Felipe Lara: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 1, No 9, 134-150

Abstract: Abstract The notions of upper and lower global directional derivatives are introduced for dealing with nonconvex and nonsmooth optimization problems. We provide calculus rules and monotonicity properties for these notions. As a consequence, new formulas for the Dini directional derivatives, radial epiderivatives and generalized asymptotic functions are given in terms of the upper and lower global directional derivatives. Furthermore, a mean value theorem, which extend the well-known Diewert’s mean value theorem for radially upper and lower semicontinuous functions, is established. We also provide necessary and sufficient optimality conditions for a point to be a local and/or global solution for the nonconvex minimization problem. Finally, applications for nonconvex and nonsmooth mathematical programming problems are also presented.

Keywords: Global derivatives; Asymptotic functions; Quasiconvexity; Nonconvex optimization; Nonsmooth optimization; 90C25; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-019-01613-9

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