Journal ArticleDOI
Shape restricted smoothing splines via constrained optimal control and nonsmooth Newton's methods
Jinglai Shen,Teresa M. Lebair +1 more
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The global convergence of the algorithm for shape restricted smoothing splines subject to general polyhedral control constraints is shown, using techniques from nonsmooth analysis and polyhedral theory.About:
This article is published in Automatica.The article was published on 2015-03-01. It has received 18 citations till now. The article focuses on the topics: Smoothing spline & Optimal control.read more
Citations
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Journal ArticleDOI
Order Restricted Statistical Inference.
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Efficient Estimation in Single Index Models through Smoothing splines
TL;DR: In this paper, the authors developed a method to compute the penalized least squares estimators (PLSEs) of the parametric and nonparametric components given independent and identically distributed (i.i.d.) data.
Journal ArticleDOI
Solution uniqueness of convex piecewise affine functions based optimization with applications to constrained ℓ1 minimization
Seyedahmad Mousavi,Jinglai Shen +1 more
TL;DR: In this article, the authors study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints.
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Exact Support and Vector Recovery of Constrained Sparse Vectors via Constrained Matching Pursuit
Jinglai Shen,Seyedahmad Mousavi +1 more
TL;DR: It is shown that exact recovery via constrained matching pursuit not only depends on a measurement matrix but also critically relies on a constraint set, and an important class of constraint sets are identified, called coordinate projection admissible set, or simply CP admissible sets.
Journal ArticleDOI
On the asymptotic behavior of the Douglas-Rachford and proximal-point algorithms for convex optimization.
Goran Banjac,John Lygeros +1 more
TL;DR: The proximal-point algorithm applied to the set of optimality conditions of the problem generates similar infeasibility certificates and is extended to real Hilbert spaces and a general nonempty closed convex set.
References
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Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Book
Spline models for observational data
TL;DR: In this paper, a theory and practice for the estimation of functions from noisy data on functionals is developed, where convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework.
Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Book
Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
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A hybrid semismooth quasi-Newton method for nonsmooth optimal control with PDEs
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Jinglai Shen,Xiao Wang +1 more