Abstract
We present a simple approach to an analysis of higher order approximations to sets and functions. The objects we study are not of a specific order; they include objects of order 2 and $m$ with $m$ not necessarily an integer. We deduce from these concepts optimality conditions of higher order and we establish some calculus rules.
Highlights
Numerous papers have been devoted to higher-order conditions in optimization. (See [3, 4], [6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [41, 42, 43, 44, 45, 46, 47, 48], [50, 51, 52, 53, 54, 55, 56, 57, 58] among many other references.) Usually they deal with a specific order of differentiability, most often the second-order
It is the purpose of the present paper to consider the case the higherorder effect is not of a specific order
We introduce higher-order derivatives for nonsmooth functions and multifunctions
Summary
Numerous papers have been devoted to higher-order conditions in optimization. (See [3, 4], [6, 7, 8], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36, 37, 38, 39], [41, 42, 43, 44, 45, 46, 47, 48], [50, 51, 52, 53, 54, 55, 56, 57, 58] among many other references.) Usually they deal with a specific order of differentiability, most often the second-order.
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