Min-max identities on boundaries of convex sets around the origin

Technical Report · Thu Jan 31 04:00:00 EST 2002

DOI:https://doi.org/10.2172/839224· OSTI ID:839224

Grcar, Joseph F ^[1]

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1. LBNL Library

Min-max and max-min identities are found for inner products on the boundaries of compact, convex sets whose interiors contain the origin. The identities resemble the minimax theorem but they are different from it. Specifically, the value of each min-max (or max-min) equals the value of a dual problem of the same type. Their solution sets can be characterized geometrically in terms of the enclosed convex sets and their polar sets. However, the solution sets need not be convex nor even connected.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 839224
• Report Number(s): LBNL--50634
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
CONVEX BOUNDARY DUALITY MIN-MAX
CONVEX MANIFOLDS
MATHEMATICAL SOLUTIONS
ORIGIN