86 research outputs found
Closing Duality Gaps of SDPs through Perturbation
Let be a primal-dual pair of SDPs with a nonzero finite
duality gap. Under such circumstances, and are weakly
feasible and if we perturb the problem data to recover strong feasibility, the
(common) optimal value function as a function of the perturbation is not
well-defined at zero (unperturbed data) since there are ``two different optimal
values'' and , where and are
the optimal values of and respectively. Thus, continuity of
is lost at zero though is continuous elsewhere. Nevertheless, we show
that a limiting version of is a well-defined monotone decreasing
continuous bijective function connecting and with
domain under the assumption that both and have
singularity degree one. The domain corresponds to directions of
perturbation defined in a certain manner. Thus, ``completely fills''
the nonzero duality gap under a mild regularity condition. Our result is tight
in that there exists an instance with singularity degree two for which
is not continuous.Comment: 26 pages. Comments welcom
Immortalization of Murine Leukocytes by Oncogenes (I) : Attempts to Immortalize Splenic Dendritic Cells Resulted in the Production of Nondendritic Transformant Cells
Associations between the orexin (hypocretin) receptor 2 gene polymorphism Val308Ile and nicotine dependence in genome-wide and subsequent association studies
Impact of the HCRTR2 gene risk variant on schizotypal personality traits (meanâÂąâSD). (DOC 54 kb
Simultaneous development of sarcoidosis and cutaneous vasculitis in a patient with refractory Crohn’s disease during infliximab therapy
Associations between the orexin (hypocretin) receptor 2 gene polymorphism Val308Ile and nicotine dependence in genome-wide and subsequent association studies
A PERTURBATION THEOREM ON POLYNOMIAL OPTIMIZATION AND ITS EXTENSIONS (The advances and applications of optimization method)
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