Approximate first-order and second-order directional derivatives f a marginal function in convex optimization
作者： J. -B. Hiriart-Urruty
DOI: 10.1007/BF00938593
关键词: Convex function 、 Pseudoconvex function 、 Convex conjugate 、 Proper convex function 、 Combinatorics 、 Subderivative 、 Convex set 、 Convex analysis 、 Mathematics 、 Logarithmically convex function
摘要: Given a convex functionf:ℝ p ×ℝ q → (−∞, +∞], the marginal function φ is defined on ℝ by φ(x)=inf{f(x, y)|y∈ℝ }. Our purpose in this paper to express approximate first-order and second-order directional derivatives of atx 0 terms those off at (x 0,y 0), wherey 0 any element for which φ(x 0)=f(x 0,y 0).
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