On Equivalent Conditions for Local Error Bounds

SEMINARIO DEL DOCTORADO DE ESTADÍSTICA, OPTIMIZACIÓN Y MATEMÁTICA APLICADA. CURSO 2015-2016

Título: On Equivalent Conditions  for Local Error Bounds

Ponentes: Prof. Dr. Xiaoqi Yang (Department of Applied Mathematics, The Hong Kong Polytechnic University)

Fecha: martes 28 de junio de 2016 a las 12:30 horas

Lugar: Sala de Seminarios del  Instituto Universitario de Investigación CIO, Edificio Torretamarit

Resumen:

In this talk we present two classes of equivalent conditions for local error bounds in finite dimensional spaces. We formulate conditions of the first class by using subderivatives, subdifferentials and strong slopes for nearby points outside the referenced set, and show that these conditions actually characterize a uniform version of the local error bound property. We demonstrate this uniformity for the max function of a finite collection of smooth functions, and as a consequence we show that quasinormality constraint qualifications guarantee the existence of local error bounds. We further present the second class of equivalent conditions for local error bounds by using the various limits defined on the boundary of the referenced set. In presenting these conditions, we exploit the variational geometry of the referenced set in a systematic way and unify some existing results in the literature. We will also discuss some further results on the error bounds.

Breve Bio:

Professor Xiaoqi Yang got his BSc in Mathematics at Jianzhu Iniversity (China) in 1982, MSc in Operations Research and Control Theory at Chinese Academy of Science in 1987, and PhD in Applied Mathematics at University of New South Wales (Australia) in 1994. His research interests are mathematical optimization, vector optimization, variational analysis, and financial optimization. In MatSciNet database we find 245 publications and 2720 cites by 889 authors. In Scopus database we also find 94 coauthors and h-index=32. He is also author of three monographies.