Hao Cheng

Works (4)

Updated: July 5th, 2023 15:59

2005 journal article

A Geometric Programming Framework for Univariate Cubic L 1 Smoothing Splines

Annals of Operations Research, 133(03-Jan), 229–248.

By: S. Fang n , H. Cheng n & J. Lavery*

author keywords: smoothing spline; geometric programming; data fitting; shape preservation; sensitivity analysis
topics (OpenAlex): Advanced Numerical Analysis Techniques; Manufacturing Process and Optimization; Probabilistic and Robust Engineering Design
TL;DR: The minimization principle for univariate cubic L1 smoothing splines results in a nondifferentiable convex optimization problem that, for theoretical treatment and algorithm design, can be formulated as a generalized geometric program. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

An Efficient Algorithm for Generating Univariate Cubic L1 Splines

Cheng, H., Fang, S.-C., & Lavery, J. E. (2004, September 17). Computational Optimization and Applications, Vol. 29, pp. 219–253.

By: H. Cheng n, S. Fang n  & J. Lavery*

author keywords: active set method; convex programming; cubic L-1 spline; geometric programming
topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Iterative Methods for Nonlinear Equations
TL;DR: An active set based algorithm for calculating the coefficients of univariate cubic L1 splines is developed that outperforms a currently widely used discretization-based primal affine algorithm. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

Shape-preserving properties of univariate cubic L1 splines

Cheng, H., Fang, S.-C., & Lavery, J. E. (2004, July 8). Journal of Computational and Applied Mathematics, Vol. 174, pp. 361–382.

By: H. Cheng n, S. Fang n  & J. Lavery*

author keywords: convexity; cubic L-1 spline; geometric programming; interpolation; linearity; shape preservation
topics (OpenAlex): Advanced Numerical Analysis Techniques; Optical measurement and interference techniques; Advanced Measurement and Metrology Techniques
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 article

Univariate cubic L 1 splines - A geometric programming approach

Cheng, H., Fang, S.-C., & Lavery, J. E. (2002, November 1). Mathematical Methods of Operations Research, Vol. 56, pp. 197–229.

By: H. Cheng n, S. Fang n  & J. Lavery

author keywords: cubic L-1 spline; geometric programming; interpolation; spline function; univariate
topics (OpenAlex): Advanced Numerical Analysis Techniques; Advanced Measurement and Metrology Techniques; Computational Geometry and Mesh Generation
TL;DR: In the natural norm for this class of problems, namely, the L1 norm of the second derivative, the geometric programming approach finds better solutions than the previously used discretization method. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

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