نتایج جستجو برای: clarke subdifferential
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We prove that the subdifferential of any semi-algebraic extended-real-valued function on Rn has n-dimensional graph. We discuss consequences for generic semi-algebraic optimization problems.
in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz. necessary optimality conditions and regularity conditions are given. our approach are based on the michel-penot subdifferential.
Our approach to the Karush-Kuhn-Tucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the Fenchel-Moreau and Dubovitskii-Milyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other hand, Proposition B.4(v) in [OSC] gives an intimate connection between the subdifferential of a fun...
Monotone operators are of basic importance in optimization as they generalize simultaneously subdifferential operators of convex functions and positive semidefinite (not necessarily symmetric) matrices. In 1970, Asplund studied the additive decomposition of a maximal monotone operator as the sum of a subdifferential operator and an “irreducible” monotone operator. In 2007, Borwein and Wiersma [...
Background: Malignant melanoma is one of the fatal cutaneous neoplasms which are curable by early diagnosis. This neoplasm is diagnosed by the biopsy of the suspected lesion. It is essential to classify the tumor based on its histology, thickness, phase of growth, level of invasion, mitotic rate, presence of regression, inflammatory infiltration and ulceration. These descriptions yield some kno...
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