Am algorithm for constrained interpolation
SIAM Journal on Scientific and Statistical Computing
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Interpolation of convex scattered data in R3 based upon edge convex minimum norm network
Journal of Approximation Theory
Implicit functions, Lipschitz maps, and stability in optimization
Mathematics of Operations Research
Piecewise smoothness, local invertibility, and parametric analysis of normal maps
Mathematics of Operations Research
Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Sensitivity analysis of composite piecewise smooth equations
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Mathematics of Operations Research
A New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
Computational Optimization and Applications
A smoothing Newton method for general nonlinear complementarity problems
Computational Optimization and Applications - Special issue on nonsmooth and smoothing methods
Solving variational inequality problems via smoothing-nonsmooth reformulations
Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
A Newton Method for Shape-Preserving Spline Interpolation
SIAM Journal on Optimization
Regularity Properties of a Semismooth Reformulation of Variational Inequalities
SIAM Journal on Optimization
On Morse Theory for Piecewise Smooth Functions
Journal of Dynamical and Control Systems
A Property of Piecewise Smooth Functions
Computational Optimization and Applications
A Property of Piecewise Smooth Functions
Computational Optimization and Applications
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As shown by an example, the integral function f : {\bb R}n → {\bb R}, defined by f(x) = ∫ab[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 {\bb R}n. 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.