TY - JOUR
AU - Lara, Felipe
AB - 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.
TI - Optimality Conditions for Nonconvex Nonsmooth Optimization via Global Derivatives
JF - Journal of Optimization Theory and Applications
DO - 10.1007/s10957-019-01613-9
DA - 2020-04-07
UR - https://www.deepdyve.com/lp/springer-journals/optimality-conditions-for-nonconvex-nonsmooth-optimization-via-global-7UHPhAA2B9
SP - 134
EP - 150
VL - 185
IS - 1
DP - DeepDyve
ER -