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M. Ghami

Nesna University College, Institute For Teacher Education, Faculty Member

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TU Delft

M. Reza Peyghami

K.N.Toosi University of Technology

University of Bergen

Guennoun Zine El Abidine

Lehigh University

Joseph Verducci

Renato Monteiro

Georgia Institute of Technology

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Papers by M. Ghami

Primal-dual algorithm for linear optimization problems based on a new class of kernel functions

by Trond Steihaug and M. Ghami

ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for... more ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for LO based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766-782, 2003. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. The iteration bound of large update interior-point methods based on these functions, are shown to be O (n1/(1+p) log n log n/isin), where p is a parameter, p isin [0,1]. We present also some numerical results which show that by using a new kernel function, the best iteration numbers was achieved in most of the test problems.

An Implementation of Interior-Point Methods Based on Kernel Functions for Linear Optimization

by M. Ghami and Trond Steihaug

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for linear optimization, based on kernel functions. We investigate the influence of the choice of kernel functions on the computational behavior of the generic primal-dual algorithm for Linear Optimization. We find that the finite kernel function gives the best results for more than 50 % of the tested problems compared to the standard log-barrier method.

Interior point methods for self-dual linear optimization problems based on kernel functions

by M. Ghami and Trond Steihaug

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for self-dual linear optimization problems based on kernel functions. We investigate the influence of the choice of the kernel functions on the theoretical complexity results and on the computational behavior of the generic primal-dual algorithm for linear optimization. We find that the finite kernel function gives the best results for more than 50% of the tested problems compared to the standard log-barrier method.

Primal-dual algorithm for linear optimization problems based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for... more ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for LO based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766-782, 2003. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. The iteration bound of large update interior-point methods based on these functions, are shown to be O (n1/(1+p) log n log n/isin), where p is a parameter, p isin [0,1]. We present also some numerical results which show that by using a new kernel function, the best iteration numbers was achieved in most of the test problems.

Primal-dual interior-point methods solver based on kernel functions for Linear Optimization

by Trond Steihaug and M. Ghami

Proceedings of the International Multiconference on Computer Science and Information Technology, IMCSIT '09, 2009

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for linear optimization, based on kernel functions. We will investigate the influence of the choice of the kernel function on the computational behavior of the generic primal-dual algorithm for Linear Optimization. We find that the finite kernel function gives the best results for more than 50 % of the tested problems compared to the standard log-barrier method.

Kernel-function Based Primal-Dual Algorithms for P * ( κ ) Linear Complementarity Problems

by Trond Steihaug and M. Ghami

RAIRO - Operations Research, 2010

ABSTRACT Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigat... more ABSTRACT Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigated a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P * (κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

A generic primal–dual interior-point method for semidefinite optimization based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

Optimization Methods and Software, 2010

A polynomial-time algorithm for linear optimization based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

Journal of Computational and Applied Mathematics, 2009

a b s t r a c t In this paper we present a class of polynomial primal-dual interior-point algorit... more a b s t r a c t In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai, M.El Ghami and C. Roos [Y.Q. Bai, M. El Ghami, and C. Roos. A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (3) (2003) 766-782].

Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

by Trond Steihaug, M. Ghami, and Guennoun Zine El Abidine

Journal of Computational and Applied Mathematics, 2012

In this paper, we present a new barrier function for primal-dual interior-point methods in linear... more In this paper, we present a new barrier function for primal-dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal-dual interiorpoint methods.

Primal-Dual IPMS for Semidefinite Optimization Based on Finite Barrier Functions

by Trond Steihaug and M. Ghami

A polynomial-time algorithm for LO based on generalized logarithmic barrier functions

by Trond Steihaug, M. Ghami, and C. Roos

We present a polynomial-time primal-dual interior-point algorithm for solving linear optimization... more We present a polynomial-time primal-dual interior-point algorithm for solving linear optimization (LO) problems, based on generalized logarithmic barrier function. The growth term depends on a parameter p ∈ [0, 1]. The kernel functions are neither self-regular nor strongly convex. The classical logarithmic barrier function occurs if p = 1. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. In order to achieve these complexity results, several new techniques had to be used for the analysis. Complexity issues are discussed and they are O n log n , and O √ n log n , for large-update and small-update methods, respectively. Numerical tests show that the iteration bounds are influenced by p. We conclude that a gap still exists between the theoretical complexity and practical behavior of the algorithm.

NIK2009-An Implementation of Interior-Point Methods Based on Kernel Functions for Linear Optimizat

by M. Ghami and Trond Steihaug

... The results from our This paper was presented at the NIK-2009 conference; see http://www.nik.... more

Primal-dual algorithm for linear optimization problems based on a new class of kernel functions

by Trond Steihaug and M. Ghami

ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for... more ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for LO based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766-782, 2003. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. The iteration bound of large update interior-point methods based on these functions, are shown to be O (n1/(1+p) log n log n/isin), where p is a parameter, p isin [0,1]. We present also some numerical results which show that by using a new kernel function, the best iteration numbers was achieved in most of the test problems.

An Implementation of Interior-Point Methods Based on Kernel Functions for Linear Optimization

by M. Ghami and Trond Steihaug

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for linear optimization, based on kernel functions. We investigate the influence of the choice of kernel functions on the computational behavior of the generic primal-dual algorithm for Linear Optimization. We find that the finite kernel function gives the best results for more than 50 % of the tested problems compared to the standard log-barrier method.

Interior point methods for self-dual linear optimization problems based on kernel functions

by M. Ghami and Trond Steihaug

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for self-dual linear optimization problems based on kernel functions. We investigate the influence of the choice of the kernel functions on the theoretical complexity results and on the computational behavior of the generic primal-dual algorithm for linear optimization. We find that the finite kernel function gives the best results for more than 50% of the tested problems compared to the standard log-barrier method.

Primal-dual algorithm for linear optimization problems based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for... more ABSTRACT In this paper we present a class of polynomial primal-dual interior-point algorithms for LO based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai M. El Ghami and C.Roos published in SIAM Journal of Optimization, 13(3):766-782, 2003. The proposed functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like the usual barrier functions. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. The iteration bound of large update interior-point methods based on these functions, are shown to be O (n1/(1+p) log n log n/isin), where p is a parameter, p isin [0,1]. We present also some numerical results which show that by using a new kernel function, the best iteration numbers was achieved in most of the test problems.

Primal-dual interior-point methods solver based on kernel functions for Linear Optimization

by Trond Steihaug and M. Ghami

Proceedings of the International Multiconference on Computer Science and Information Technology, IMCSIT '09, 2009

In this paper we present the theory and practical aspects of implementing the path following inte... more In this paper we present the theory and practical aspects of implementing the path following interior point methods for linear optimization, based on kernel functions. We will investigate the influence of the choice of the kernel function on the computational behavior of the generic primal-dual algorithm for Linear Optimization. We find that the finite kernel function gives the best results for more than 50 % of the tested problems compared to the standard log-barrier method.

Kernel-function Based Primal-Dual Algorithms for P * ( κ ) Linear Complementarity Problems

by Trond Steihaug and M. Ghami

RAIRO - Operations Research, 2010

ABSTRACT Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigat... more ABSTRACT Recently, [Y.Q. Bai, M. El Ghami and C. Roos, SIAM J. Opt. 15 (2004) 101–128] investigated a new class of kernel functions which differs from the class of self-regular kernel functions. The class is defined by some simple conditions on the growth and the barrier behavior of the kernel function. In this paper we generalize the analysis presented in the above paper for P * (κ) Linear Complementarity Problems (LCPs). The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.

A generic primal–dual interior-point method for semidefinite optimization based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

Optimization Methods and Software, 2010

A polynomial-time algorithm for linear optimization based on a new class of kernel functions

by Cornelis Roos, Trond Steihaug, and M. Ghami

Journal of Computational and Applied Mathematics, 2009

a b s t r a c t In this paper we present a class of polynomial primal-dual interior-point algorit... more a b s t r a c t In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the class of finite kernel functions by Y.Q. Bai, M.El Ghami and C. Roos [Y.Q. Bai, M. El Ghami, and C. Roos. A new efficient large-update primal-dual interior-point method based on a finite barrier, SIAM Journal on Optimization, 13 (3) (2003) 766-782].

Interior-point methods for linear optimization based on a kernel function with a trigonometric barrier term

by Trond Steihaug, M. Ghami, and Guennoun Zine El Abidine

Journal of Computational and Applied Mathematics, 2012

In this paper, we present a new barrier function for primal-dual interior-point methods in linear... more In this paper, we present a new barrier function for primal-dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal-dual interiorpoint methods.

Primal-Dual IPMS for Semidefinite Optimization Based on Finite Barrier Functions

by Trond Steihaug and M. Ghami

A polynomial-time algorithm for LO based on generalized logarithmic barrier functions

by Trond Steihaug, M. Ghami, and C. Roos

We present a polynomial-time primal-dual interior-point algorithm for solving linear optimization... more We present a polynomial-time primal-dual interior-point algorithm for solving linear optimization (LO) problems, based on generalized logarithmic barrier function. The growth term depends on a parameter p ∈ [0, 1]. The kernel functions are neither self-regular nor strongly convex. The classical logarithmic barrier function occurs if p = 1. The goal of this paper is to investigate such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. In order to achieve these complexity results, several new techniques had to be used for the analysis. Complexity issues are discussed and they are O n log n , and O √ n log n , for large-update and small-update methods, respectively. Numerical tests show that the iteration bounds are influenced by p. We conclude that a gap still exists between the theoretical complexity and practical behavior of the algorithm.

NIK2009-An Implementation of Interior-Point Methods Based on Kernel Functions for Linear Optimizat

by M. Ghami and Trond Steihaug

... The results from our This paper was presented at the NIK-2009 conference; see http://www.nik.... more