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- Chek Beng Chua
- Foundations of Computational Mathematics
- 2007

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone K, a logarithmically homogeneous self-concordant barrier for K and any positive real number r ≤ 1, we associate, with each direction x ∈ K, a second-order cone K̂r(x) containing K. We show that K is the intersection of the… (More)

- Chek Beng Chua
- SIAM Journal on Optimization
- 2003

T -algebras are nonassociative algebras defined by Vinberg in the early 1960s for the purpose of studying homogeneous cones. Vinberg defined a cone K(A) for each T -algebra A and proved that every homogeneous cone is isomorphic to one such K(A). We relate each T -algebra A with a space of linear operators in such a way that K(A) is isomorphic to the cone of… (More)

- Chek Beng Chua, Levent Tunçel
- Math. Program.
- 2008

We consider two notions for the representations of convex cones: G-representation and liftedG-representation. The former represents a convex cone as a slice of another; the latter allows in addition, the usage of auxiliary variables in the representation. We first study the basic properties of these representations. We show that some basic properties of… (More)

- Chek Beng Chua, Peng Yi
- SIAM Journal on Optimization
- 2010

In this paper, we introduce a new P -type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P -type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically.

Abstract. We study the uniform nonsingularity property recently proposed by the authors and present its applications to nonlinear complementarity problems over a symmetric cone. In particular, by addressing theoretical issues such as the existence of Newton directions, the boundedness of iterates and the nonsingularity of B-subdifferentials, we show that… (More)

- Chek Beng Chua
- SIAM Journal on Optimization
- 2006

The notion of weighted centers is essential in V-space interior-point algorithms for linear programming. Although there were some successes in generalizing this notion to semidefinite programming via weighted center equations, we still do not have a generalization that preserves two important properties — 1) each choice of weights uniquely determines a pair… (More)

- Chek Beng Chua
- SIAM Journal on Optimization
- 2009

Three primal-dual interior-point algorithms for homogeneous cone programming are presented. They are a short-step algorithm, a large-update algorithm, and a predictor-corrector algorithm. These algorithms are described and analyzed based on a characterization of homogeneous cone via T -algebra. The analysis show that the algorithms have polynomial iteration… (More)

Two important topics in the study of Quadratically Constrained Quadratic Programming (QCQP) are how to exactly solve a QCQP with few constraints in polynomial time and how to find an inexpensive and strong relaxation bound for a QCQP with many constraints. In this thesis, we first review some important results on QCQP, like the S-Procedure, and the strength… (More)

- CHEK BENG CHUA, PENG YI
- 2009

In this paper, we introduce a new P -type condition for nonlinear functions defined over Euclidean Jordan algebras, and study a continuation method for nonlinear complementarity problems over symmetric cones. This new P -type condition represents a new class of nonmonotone nonlinear complementarity problems that can be solved numerically.

- Chek Beng Chua, Zhen Li
- SIAM Journal on Optimization
- 2013

We present a new barrier-based method of constructing smoothing approximations for the Euclidean projector onto closed convex cones. These smoothing approximations are used in a smoothing proximal point algorithm to solve monotone nonlinear complementarity problems (NCPs) over a convex cones via the normal map equation. The smoothing approximations allow… (More)