Exact order of Hoffman’s error bounds for elliptic quadratic inequalities derived from vector-valued Chebyshev approximation

2000 ◽  
Vol 88 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Martin Bartelt ◽  
Wu Li
Keyword(s):  
Error Bounds ◽  
Chebyshev Approximation ◽  
Exact Order ◽  
Quadratic Inequalities ◽  
Vector Valued

Application of integral operator for vector-valued regression learning

2015 ◽  
Vol 13 (06) ◽  
pp. 1550047 ◽  
Author(s):  
Yuanxin Ma ◽  
Hongwei Sun
Keyword(s):  
Hilbert Space ◽  
Integral Operator ◽  
Error Bounds ◽  
Learning Algorithm ◽  
Learning Performance ◽  
Operator Technique ◽  
Output Data ◽  
Learning Rates ◽  
Regression Learning ◽  
Vector Valued

In this paper, the regression learning algorithm with vector-valued RKHS is studied. We motivate the need for extending learning theory of scalar-valued functions and analze the learning performance. In this setting, the output data are from a Hilbert space [Formula: see text], the associated RKHS consists of functions with values lie in [Formula: see text]. By providing mathematical aspects of vector-valued integral operator [Formula: see text], the capacity independent error bounds and learning rates are derived by means of the integral operator technique.

Stability of error bounds for conic subsmooth inequalities

2019 ◽  
Vol 25 ◽  
pp. 55
Author(s):  
Xi Yin Zheng ◽  
Kung-Fu Ng
Keyword(s):  
Error Bounds ◽  
Perturbation Analysis ◽  
Small Perturbations ◽  
Convexity Assumption ◽  
Constraint Systems ◽  
Inequality Systems ◽  
The Stability ◽  
Vector Valued Functions ◽  
Analysis Of Error ◽  
Vector Valued

Under either linearity or convexity assumption, several authors have studied the stability of error bounds for inequality systems when the concerned data undergo small perturbations. In this paper, we consider the corresponding issue for a more general conic inequality (most of the constraint systems in optimization can be described by an inequality of this type). In terms of coderivatives for vector-valued functions, we study perturbation analysis of error bounds for conic inequalities in the subsmooth setting. The main results of this paper are new even in the convex/smooth case.

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