Lipschitz Properties of Solution in Mathematical Programming.

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Abstract:

In this paper, we are concerned with the behaviour of the solutions of problems and also with the Lipschitzian dependence of the set of solutions with respect to the parameter alpha. The paper is organized as follows. The main theorems of the paper are stated. Sufficient conditions are give to have 1 local uniqueness of solutions and 2 Lipschitzian dependence of the solution with respect to the parameter alpha. The proofs of the theorems are given. The main tool, in this analysis, is an implicit function theorem for Lipschitzian mappings due to Clarke see also Hiriart-Urruty. The main idea is to write the generalized equation as a system of Lipschitzian mapping, to which Clarkes implicit function can be applied. The notion of generalized derivative of the projection mapping on a convex are of particular use.

Author(s):
Cornet, Bernard ; Laroque, Guy
Author Organization(s):
STANFORD UNIV CA INST FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES
Descriptive Note:
Technical rept.,
Pagination:
0022

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release

RECORD

Collection: TR
Identifying Numbers
Report Number(s):
TR-369
Contract/Grant Number(s):
N00014-79-C-0685
 Subject Terms
Joint Capability Areas:
JCA_5.3_Planning; JCA_5_Command and Control; JCA_1.2_Force Preparation; JCA_1_Force Support; JCA_1.2.3_Educating
Communities of Interest:
No COI(s) Identified
Descriptor(s):
*MATHEMATICAL PROGRAMMING, *MAPPING(TRANSFORMATIONS), PARAMETERS, PROBLEM SOLVING, VARIATIONS, SOLUTIONS(GENERAL), PERTURBATIONS, NONLINEAR PROGRAMMING, INEQUALITIES
Field(s)/Group(s):
Theoretical Mathematics
Keyword(s):
Lipschitz mapping
Report Date:
1982 Aug 01