Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29263
Title: A strongly semismooth integral function and its application
Authors: Qi, L 
Yin, H
Keywords: Generalized Newton method
Integral function
Piecewise smoothness
Quadratic convergence
Strong semismoothness
Issue Date: 2003
Source: Computational optimization and applications, 2003, v. 25, no. 1-3, p. 223-246 How to cite?
Journal: Computational Optimization and Applications 
Abstract: As shown by an example, the integral function f : ℝn → ℝ, defined by f(x) = ∫a b[B(x, t)]+g(t)dt, may not be a strongly semismooth function, even if g(t) ≡ 1 and B is a quadratic polynomial with respect to t and infinitely many times smooth with respect to x. We show that f is a strongly semismooth function if g is continuous and B is affine with respect to t and strongly semismooth with respect to x, i.e., B(x, t) = u(x)t + v(x), where u and v are two strongly semismooth functions in ℝn. We also show that f is not a piecewise smooth function if u and v are two linearly independent linear functions, g is continuous and g ≢ 0 in [a, b], and n ≥ 2. We apply the first result to the edge convex minimum norm network interpolation problem, which is a two-dimensional interpolation problem.
URI: http://hdl.handle.net/10397/29263
ISSN: 0926-6003
DOI: 10.1023/A:1022969507994
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