Mathematical Programming problems with Semilocally Convex Functions on Banach Spaces
碩士 === 東海大學 === 應用數學研究所 === 83 === Convexity is useful in many aspects of mathematical programming. so there are various generalizations of convexity like quasiconvex and pseudoconvex , invex and preinvex etc. Which are puite lose to convex...
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| Format: | Others |
| Language: | en_US |
| Published: |
1995
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| Online Access: | http://ndltd.ncl.edu.tw/handle/88268035891884094871 |
| Summary: | 碩士 === 東海大學 === 應用數學研究所 === 83 === Convexity is useful in many aspects of mathematical
programming. so there are various generalizations of convexity
like quasiconvex and pseudoconvex , invex and preinvex etc.
Which are puite lose to convexity. These generalization have
good behavior like convex case. In this thesis, we study the
mathematical programming prob- lem (P) with semilocally convex
functions on locally starshaped set in a Banach space. We
formulate a perturbed problem (Pz) of (P). It can be shown that
the perturbed functions is still a semiocally convex
programming problem defind on a locally star- shaped set. We
show that the perturbed problem (Pz) is stable at the origin z
= 0 (zero vector) if and only if the perturb- ed function has
a nonempty subdifferential. It is proved that the semilocally
convex programming problem (P) is solvable if and only if the
Lagrangian of (P) has a saddle point. We also derive the dual
problem of (P), and show that the duality theor- em is valid in
semilocally convex programming problem.
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