Weak Tangent Cones and Optimization in a Banach Space | Zendy

Jonathan M. Borwein | Zendy

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Weak Tangent Cones and Optimization in a Banach Space

Author(s) -

Jonathan M. Borwein

Publication year - 1978

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/0316034

Subject(s) - tangent cone , mathematics , tangent , banach space , cone (formal languages) , tangent space , constraint (computer aided design) , order (exchange) , space (punctuation) , tangent vector , mathematical analysis , pure mathematics , geometry , computer science , algorithm , finance , economics , operating system

A general notion of a r-tangent cone is introduced and developed for optimization purposes. This includes as special cases both the weak and strong tangent cones that appear in the literature. First order conditions with and without constraint qualification are examined and particular examples are provided to demonstrate that these conditions properly subsume those previously in the literature. Emphasis is placed on weak Kuhn–Tucker sufficiency conditions

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