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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 conê K r (x) containing K. We show that K is the intersection of the… (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)

- 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.

- Chek Beng Chua
- SIAM Journal on Optimization
- 2003

Title Relating homogeneous cones and positive definite cones via T-algebras.(Published version) Abstract. 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… (More)

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

We consider two notions for the representations of convex cones: G-representation and lifted-G-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, 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)

- Chek Beng Chua
- Math. Program.
- 2008

The purpose of this paper is twofold. Firstly, we show that every Cholesky-based weighted central path for semidefinite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of… (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
- 2006

We present a target-following framework for semidefinite programming, which generalizes the target-following framework for linear programming. We use this framework to build weighted path-following interior-point algorithms of three distinct flavors: short-step, predictor-corrector, and large-update. These algorithms have worse-case iteration bounds that… (More)