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Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes theâ€¦ (More)

- John T. Lonsdale, Jeffrey A. Thomas, +124 authors Helen F Moore
- Nature Genetics
- 2013

Genome-wide association studies have identified thousands of loci for common diseases, but, for the majority of these, the mechanisms underlying disease susceptibility remain unknown. Most associatedâ€¦ (More)

- Liqun Qi
- Math. Oper. Res.
- 1993

- Liqun Qi
- J. Symb. Comput.
- 2005

In this paper, we define the symmetric hyperdeterminant, eigenvalues and E-eigenvalues of a real supersymmetric tensor. We show that eigenvalues are roots of a one-dimensional polynomial, and whenâ€¦ (More)

- Xiaojun Chen, Liqun Qi, Defeng Sun
- Math. Comput.
- 1998

The smoothing Newton method for solving a system of nonsmooth equations F (x) = 0, which may arise from the nonlinear complementarity problem, the variational inequality problem or other problems,â€¦ (More)

- Liqun Qi, Defeng Sun, Guanglu Zhou
- Math. Program.
- 2000

In this paper we take a new look at smoothing Newton methods for solving the nonlinear complementarity problem (NCP) and the box constrained variational inequalities (BVIs). Instead of using anâ€¦ (More)

- Chen Ling, Jiawang Nie, Liqun Qi, Yinyu Ye
- SIAM Journal on Optimization
- 2009

This paper studies the so-called bi-quadratic optimization over unit spheres min xâˆˆRn,yâˆˆRm âˆ‘ 1â‰¤i,kâ‰¤n, 1â‰¤j,lâ‰¤m bijklxiyjxkyl subject to â€–xâ€– = 1, â€–yâ€– = 1. We show that this problem is NP-hard and thereâ€¦ (More)

- Francisco Facchinei, Houyuan Jiang, Liqun Qi
- Math. Program.
- 1999

The mathematical program with equilibrium constraints (MPEC) is an optimization problem with variational inequality constraints. MPEC problems include bilevel programming problems as a particularâ€¦ (More)

- Xiaojun Chen, Zuhair Nashed, Liqun Qi
- SIAM J. Numerical Analysis
- 2000

We consider superlinearly convergent analogues of Newton methods for nondifferentiable operator equations in function spaces. The superlinear convergence analysis of semismooth methods forâ€¦ (More)

- Edward S. Hui, Matthew M. Cheung, Liqun Qi, Ed X. Wu
- NeuroImage
- 2008

MR diffusion kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean kurtosis, the directionally averaged kurtosis, has been shown toâ€¦ (More)