Hankel Matrix Rank Minimization with Applications to System Identification and Realization
- Maryam Fazel, Ting Kei Pong, Defeng Sun, P. Tseng
- Computer Science, MathematicsSIAM Journal on Matrix Analysis and Applications
- 11 July 2013
We introduce a flexible optimization framework for nuclear norm minimization of matrices with linear structure, including Hankel, Toeplitz, and moment structures and catalog applications from diverse…
A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
- L. Qi, Defeng Sun, Guanglu Zhou
- MathematicsMathematical programming
- 2000
It is proved that three most often used Gabriel-Moré smoothing functions can generate strongly semismooth functions, which play a fundamental role in establishing superlinear and quadratic convergence of the new smoothing Newton methods.
A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
- H. Qi, Defeng Sun
- Mathematics, Computer ScienceSIAM Journal on Matrix Analysis and Applications
- 1 June 2006
The quadratic convergence of the proposed Newton method for the nearest correlation matrix problem is proved, which confirms the fast convergence and the high efficiency of the method.
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
- Xinyuan Zhao, Defeng Sun, K. Toh
- MathematicsSIAM Journal on Optimization
- 2010
This work considers a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods and shows that the positive definiteness of the generalized Hessian of the objective function in these inner problems is equivalent to the constraint nondegeneracy of the corresponding dual problems.
Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
- Xiaojun Chen, L. Qi, Defeng Sun
- MathematicsMathematics of Computation
- 1 April 1998
It is shown that for box constrained variational inequalities if the involved function is P- uniform, the iteration sequence generated by the smoothing Newton method will converge to the unique solution of the problem globally and superlinearly (quadratically).
SDPNAL$$+$$+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
- Liuqin Yang, Defeng Sun, K. Toh
- Computer ScienceMathematical Programming Computation
- 4 June 2014
SDPNAL appears to be the only viable method currently available to solve large scale SDPs arising from rank-1 tensor approximation problems constructed by Nie and Wang.
The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications
- Defeng Sun
- MathematicsMathematics of Operations Research
- 1 November 2006
For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson's constraint qualification, the following conditions are proved to be equivalent: the strong…
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
- Defeng Sun, Jie Sun
- MathematicsMathematics of Operations Research
- 1 May 2008
It is shown that many optimization-related classical results in the symmetric matrix space can be generalized within this framework and the metric projection operator over any symmetric cone defined in a Euclidean Jordan algebra is shown to be strongly semismooth.
A Majorized Penalty Approach for Calibrating Rank Constrained Correlation Matrix Problems
- Yan Gao, Defeng Sun
- Mathematics, Computer Science
- 2010
This paper first considers a penalized version of this problem and applies the essential ideas of the majorization method to the penalized problem by solving iteratively a sequence of least squares correlation matrix problems without the rank constraint.
Semismooth Matrix-Valued Functions
- Defeng Sun, Jie Sun
- MathematicsMathematics of Operations Research
- 1 February 2002
The first part of this paper discusses basic properties such as the generalized derivative, Rademacher's theorem, B-derivative, directional derivative, and semismoothness, and shows that the matrix absolute-value function, the matrix semidefinite-projection function, and the matrix projective residual function are stronglySemismooth.
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