PARTIAL SECOND-ORDER SUBDIFFERENTIALS OF ∂-PROX- REGULAR FUNCTIONS

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NADI S.; VAKILI J.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2017 | Volume:3 | Issue:10 Page(s): 87-94

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Information Journal Paper

Title

PARTIAL SECOND-ORDER SUBDIFFERENTIALS OF ∂-PROX- REGULAR FUNCTIONS

Author(s)

NADI S. | VAKILI J. | Issue Writer Certificate

Keywords

PROX-REGULAR FUNCTIONSQ1

MAXIMAL MONOTONE MAPPINGQ1

PARTIAL SECOND ORDER SUB-DIFFERENTIALSQ1

CODERIVATIVEQ1

VARIATIONAL ANALYSISQ1

Abstract

Although PROX-REGULAR FUNCTIONS in general are nonconvex, they possess properties that one would expect to find in convex or lower- C 2 functions. The class of proxregular functions covers all convex functions, lower- C 2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal sub-differential. Then, the definition of PROX-REGULAR FUNCTIONS have been developed in Banach and Hilbert spaces. In this paper, the parametric proxregular functions are defined using limiting sub-differentials. Also, a partial second order sub-differential is defined here for extended real valued functions of two variables corresponding to its variables through CODERIVATIVEs of first-order partial sub-differential mappings. Then, relations between maximal monotonicity of the partial first-order sub-differentials of these functions and the positive semi definiteness of the CODERIVATIVEs of partial first order sub-differential mapping are investigated. Finally, we present necessary and sufficient conditions for ¶ -proxregular functions to be convex based on positive-semi definiteness of the partial second-order sub-differentials mappings.

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APA: Copy

NADI, S., & VAKILI, J.. (2017). PARTIAL SECOND-ORDER SUBDIFFERENTIALS OF ∂-PROX- REGULAR FUNCTIONS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 3(10), 87-94. SID. https://sid.ir/paper/257309/en

Vancouver: Copy

NADI S., VAKILI J.. PARTIAL SECOND-ORDER SUBDIFFERENTIALS OF ∂-PROX- REGULAR FUNCTIONS. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2017;3(10):87-94. Available from: https://sid.ir/paper/257309/en

IEEE: Copy

S. NADI, and J. VAKILI, “PARTIAL SECOND-ORDER SUBDIFFERENTIALS OF ∂-PROX- REGULAR FUNCTIONS,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 3, no. 10, pp. 87–94, 2017, [Online]. Available: https://sid.ir/paper/257309/en

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