Mathematical Programming problems with Semilocally Convex Functions on Banach Spaces

• Main Authors: Chang, Shin-Yeu, 張勳宇
• Other Authors: Lai, Hang-Chin
• Format: Others
• Language: en_US
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/88268035891884094871

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.