Luo, Z. Q.
Overview
Works:  9 works in 17 publications in 2 languages and 26 library holdings 

Roles:  Author 
Classifications:  TJ217.5, 519.76 
Publication Timeline
.
Most widely held works by
Z. Q Luo
On the complexity of a column generation algorithm for convex or quasiconvex feasability problems by
J.L Goffin(
Book
)
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Data fusion with minimal communication by
ZhiQuan Luo(
Book
)
4 editions published between 1991 and 1993 in English and held by 5 WorldCat member libraries worldwide
4 editions published between 1991 and 1993 in English and held by 5 WorldCat member libraries worldwide
New error bounds for the linear complementarity problem by
Z. Q Luo(
Book
)
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
When the matrix associated with the LCP is nondegenerate, the new error bound is in fact global. This extends the error bound result [MaP90] for the LCP with a Pmatrix."
2 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
When the matrix associated with the LCP is nondegenerate, the new error bound is in fact global. This extends the error bound result [MaP90] for the LCP with a Pmatrix."
Further complexity analysis of a primaldual column generation algorithm for convex or quasiconvex feasibility problems by
J.L Goffin(
Book
)
2 editions published in 1993 in French and English and held by 4 WorldCat member libraries worldwide
2 editions published in 1993 in French and English and held by 4 WorldCat member libraries worldwide
On the computational complexity of the maximum trade problem by
David Lorge Parnas(
Book
)
1 edition published in 1992 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 3 WorldCat member libraries worldwide
Conic convex programming and selfdual embedding by
Z.Q Luo(
Book
)
2 editions published in 1998 in English and held by 2 WorldCat member libraries worldwide
How to initialize an algorithm to solve an optimization problem is of great theoretical and practical importance. In the simplex method for linear programming this issue is resolved by either the twophase approach or using the socalled big $M$ technique. In the interior point method, there is a more elegant way to deal with the initialization problem, viz. the selfdual embedding technique proposed by Ye, Todd and Mizuno. For linear programming this technique makes it possible to identify an optimal solution or conclude the problem to be infeasible/unbounded by solving its embedded selfdual problem. The embedded selfdual problem has a trivial initial solution and has the same structure as the original problem. Hence, it eliminates the need to consider the initialization problem at all. In this paper, we extend this approach to solve general conic convex programming, including semidefinite programming. Since a nonlinear conic convex programming problem may lack the socalled strict complementarity property, it causes difficulties in identifying solutions for the original problem, based on solutions for the embedded selfdual system. We provide numerous examples from semidefinite programming to illustrate various possibilities which have no analogue in the linear programming case
2 editions published in 1998 in English and held by 2 WorldCat member libraries worldwide
How to initialize an algorithm to solve an optimization problem is of great theoretical and practical importance. In the simplex method for linear programming this issue is resolved by either the twophase approach or using the socalled big $M$ technique. In the interior point method, there is a more elegant way to deal with the initialization problem, viz. the selfdual embedding technique proposed by Ye, Todd and Mizuno. For linear programming this technique makes it possible to identify an optimal solution or conclude the problem to be infeasible/unbounded by solving its embedded selfdual problem. The embedded selfdual problem has a trivial initial solution and has the same structure as the original problem. Hence, it eliminates the need to consider the initialization problem at all. In this paper, we extend this approach to solve general conic convex programming, including semidefinite programming. Since a nonlinear conic convex programming problem may lack the socalled strict complementarity property, it causes difficulties in identifying solutions for the original problem, based on solutions for the embedded selfdual system. We provide numerous examples from semidefinite programming to illustrate various possibilities which have no analogue in the linear programming case
An optimum complete orthonormal basis for signal analysis and design by
Q Jin(
Book
)
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
New error bounds for the linear complimentarity problem by University of WisconsinMadison(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Matrix convex functions with applications to weighted centers for semidefinite programming by
Jan Brinkhuis(
)
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
In this paper, we develop various calculus rules for general smooth matrixvalued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function log X to study a new notion of weighted convex centers for semidefinite programming (SDP) and show that, with this definition, some known properties of weighted centers for linear programming can be extended to SDP. We also show how the calculus rules for matrix convex functions can be used in the implementation of barrier methods for optimization problems involving nonlinear matrix functions
1 edition published in 2005 in English and held by 0 WorldCat member libraries worldwide
In this paper, we develop various calculus rules for general smooth matrixvalued functions and for the class of matrix convex (or concave) functions first introduced by Loewner and Kraus in 1930s. Then we use these calculus rules and the matrix convex function log X to study a new notion of weighted convex centers for semidefinite programming (SDP) and show that, with this definition, some known properties of weighted centers for linear programming can be extended to SDP. We also show how the calculus rules for matrix convex functions can be used in the implementation of barrier methods for optimization problems involving nonlinear matrix functions
Audience Level
0 

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Related Identities
 Groupe d'études et de recherche en analyse des décisions (Montréal, Québec)
 McMaster University Communications Research Laboratory
 Ye, Yinyu
 Tsitsiklis, John N.
 Goffin, J.L (JeanLouis) Author
 Goffin, J.L (JeanLouis) Author
 Ye, Y. (Yinyu)
 Parnas, D. L. (David Lorge) Author
 Trio
 Center for Intelligent Control Systems (U.S.)