Abstract
In this paper, a new generalized second-order directional derivative and a set-valued generalized Hessian are introudced for C1,1 functions in real Banach spaces. It is shown that this set-valued generalized Hessian is single-valued at a point if and only if the function is twice weakly Gateaux differentiable at the point and that the generalized second-order directional derivative is upper semi-continuous under a regularity condition. Various generalized calculus rules are also given for C1,1 functions. The generalized second-order directional derivative is applied to derive second-order necessary optimality conditions for mathematical programming problems.
Original language | English |
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Pages (from-to) | 165-185 |
Number of pages | 21 |
Journal | Optimization |
Volume | 26 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 1 Jan 1992 |
Externally published | Yes |
Keywords
- C functions 1,1
- generalized second-order derivatives
- nonsmooth analysis
- second-order necessary conditions
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics