Well-Posedness Properties In Variational Analysis And Its Applications
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چکیده
WELL-POSEDNESS PROPERTIES IN VARIATIONAL ANALYSIS AND ITSAPPLICATIONSbyWEI OUYANGAugust 2015Advisor: Prof. Boris S. MordukhovichMajor: Mathematics (Applied)Degree: Doctor of PhilosophyThis dissertation focuses on the study and applications of some significant properties inwell-posedness and sensitivity analysis, among which the notions of uniform metric regularity,higher-order metric subregularity and its strong subregularity counterpart play an essentialrole in modern variational analysis. We derived verifiable sufficient conditions and necessaryconditions for those notions in terms of appropriate generalized differential as well as geometricconstructions of variational analysis. Concrete examples are provided to illustrate the behaviorand compare the results. Optimality conditions of parametric variational systems (PVS) underequilibrium constraints are also investigated via the terms of coderivatives. We derived necessaryoptimality and suboptimality conditions for various problems of constrained optimization andequilibria such as MPECs with amenable/full rank potentials and EPECs with closed preferencesin finite-dimensional spaces.
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تاریخ انتشار 2016