Minimizing Irregular Convex Functions: Ulam Stability for Approximate Minima
نویسندگان
چکیده
منابع مشابه
Minimizing Irregular Convex Functions: Ulam Stability for Approximate Minima
The main concern of this article is to study Ulam stability of the set of ε-approximate minima of a proper lower semicontinuous convex function bounded below on a real normed space X, when the objective function is subjected to small perturbations (in the sense of Attouch & Wets). More precisely, we characterize the class all proper lower semicontinuous convex functions bounded below such that ...
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When a convex function f : D → R is disturbed by some nonlinear bounded perturbation p : D → R, the arising function f̃ = f + p is no more convex and its local minimizers are no more global minimizers. In order to get some similar properties for f̃ , we use a convexity modulus of f named h1 and its generalized inverse function h−1 1 , and show that f̃ is outer γ-convex for any γ ≥ γ∗ := h−1 1 ( 2 ...
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A function on R with multiple local minima is approximated from below, via linear programming, by a linear combination of convex kernel functions using sample points from the given function. The resulting convex kernel underestimator is then minimized, using either a linear equation solver for a linear-quadratic kernel or by a Newton method for a Gaussian kernel, to obtain an approximation to a...
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ژورنال
عنوان ژورنال: Set-Valued and Variational Analysis
سال: 2010
ISSN: 1877-0533,1877-0541
DOI: 10.1007/s11228-010-0153-9