Regularity Conditions via Quasi-Relative Interior in Convex Programming

2008 ◽  
Vol 19 (1) ◽  
pp. 217-233 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Ernö Robert Csetnek ◽  
Gert Wanka
Keyword(s):  
Convex Programming ◽  
Relative Interior ◽  
Regularity Conditions ◽  
Quasi Relative Interior

scholarly journals Existence Theorems for Vector Equilibrium Problems via Quasi-Relative Interior

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Capătă Adela Elisabeta
Keyword(s):  
Equilibrium Problems ◽  
Existence Theorems ◽  
Relative Interior ◽  
Vector Equilibrium Problems ◽  
Quasi Relative Interior ◽  
Vector Equilibrium ◽  
Convexity Assumptions

The aim of this paper is to present new existence theorems for solutions of vector equilibrium problems, by using weak interior type conditions and weak convexity assumptions.

scholarly journals ON A SEPARATION THEOREM INVOLVING THE QUASI-RELATIVE INTERIOR

2007 ◽  
Vol 50 (3) ◽  
pp. 605-610 ◽  
Author(s):  
F. Cammaroto ◽  
B. Di Bella
Keyword(s):  
Separation Theorem ◽  
Relative Interior ◽  
Separation Theorems ◽  
Quasi Relative Interior

AbstractWe establish two separation theorems in which the classic interior is replaced by the quasi-relative interior.

Mixed H2/H∞ control via convex programming

1991 ◽  
Author(s):  
Mario A. Rotea ◽  
Pramod P. Khargonekar
Keyword(s):  
Convex Programming

Standard Asymptotic Theory

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Statistical Significance ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Asymptotic Results ◽  
Ml Estimation ◽  
True Parameter ◽  
Log Likelihood ◽  
Ml Estimator

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

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