Mathematical Programming

, Volume 13, Issue 1, pp 183–199 | Cite as

Multivalued convexity and optimization: A unified approach to inequality and equality constraints

  • J. Borwein
Article

Abstract

Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes.

Key words

Multivalued convexity Quasi-convexity Convex programming Alternative theorems Generalized Slater condition Transposition theorems Lagrange multipliers 

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Copyright information

© The Mathematical Programming Society 1977

Authors and Affiliations

  • J. Borwein
    • 1
  1. 1.Dalhousie UniversityHalifaxCanada

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