Superlinear Noninterior One-Step Continuation Method for Monotone LCP in the Absence of Strict Complementarity

In this paper, by using a modified smoothing function, we propose a new continuation method for complementarity problems with R0-function and P0-function in the absence of strict complementarity. At each iteration, the continuation method solves one linear system of equations and performs one line search. When the underlying mapping is both a P0-function and a R0-function and its Hessian is Lipschitz continuous, we prove the global convergence of the new method. The new method also has global Q-linear and local Q-quadratical convergence rates under the same conditions.

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AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595911003284 ◽

2011 ◽

Vol 28 (03) ◽

pp. 361-399 ◽

Cited By ~ 1

Author(s):

CHUNGEN SHEN ◽

WENJUAN XUE ◽

DINGGUO PU

Keyword(s):

Linear Independence ◽

Linear Equations ◽

Coefficient Matrix ◽

Active Set ◽

Strict Complementarity ◽

Complementarity Condition ◽

Sequential Systems ◽

Computational Effect ◽

Systems Of Linear Equations ◽

One Step

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.

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One-step quadratic convergence of noninterior continuation method for NCP

Chinese Science Bulletin ◽

10.1007/bf02886340 ◽

1999 ◽

Vol 44 (20) ◽

pp. 1858-1862 ◽

Cited By ~ 2

Author(s):

Naihua Xiu

Keyword(s):

Quadratic Convergence ◽

Continuation Method ◽

One Step

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An Interactive Minicomputer Program for the Indexing and Simulation of Electron Diffraction Patterns

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100092670 ◽

1976 ◽

Vol 34 ◽

pp. 542-543

Author(s):

R.P. Goehner ◽

W.T. Hatfield ◽

Prakash Rao

Keyword(s):

Electron Diffraction ◽

Real Time ◽

Pattern Analysis ◽

Flow Diagram ◽

Hard Copy ◽

Time Analysis ◽

Real Time Analysis ◽

Transmission Electron ◽

One Step ◽

Diffraction Patterns

Computer programs are now available in various laboratories for the indexing and simulation of transmission electron diffraction patterns. Although these programs address themselves to the solution of various aspects of the indexing and simulation process, the ultimate goal is to perform real time diffraction pattern analysis directly off of the imaging screen of the transmission electron microscope. The program to be described in this paper represents one step prior to real time analysis. It involves the combination of two programs, described in an earlier paper(l), into a single program for use on an interactive basis with a minicomputer. In our case, the minicomputer is an INTERDATA 70 equipped with a Tektronix 4010-1 graphical display terminal and hard copy unit.A simplified flow diagram of the combined program, written in Fortran IV, is shown in Figure 1. It consists of two programs INDEX and TEDP which index and simulate electron diffraction patterns respectively. The user has the option of choosing either the indexing or simulating aspects of the combined program.

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Nutrient-regulated gene expression in eukaryotes

Biochemical Society Symposium ◽

10.1042/bss0730085 ◽

2006 ◽

Vol 73 ◽

pp. 85-96 ◽

Cited By ~ 8

Author(s):

Richard J. Reece ◽

Laila Beynon ◽

Stacey Holden ◽

Amanda D. Hughes ◽

Karine Rébora ◽

...

Keyword(s):

Gene Expression ◽

Rna Polymerase ◽

Rna Polymerase Ii ◽

Transcriptional Control ◽

Direct Interaction ◽

Signalling Pathways ◽

A Cell ◽

One Step ◽

Higher Eukaryotes ◽

Regulated Gene Expression

The recognition of changes in environmental conditions, and the ability to adapt to these changes, is essential for the viability of cells. There are numerous well characterized systems by which the presence or absence of an individual metabolite may be recognized by a cell. However, the recognition of a metabolite is just one step in a process that often results in changes in the expression of whole sets of genes required to respond to that metabolite. In higher eukaryotes, the signalling pathway between metabolite recognition and transcriptional control can be complex. Recent evidence from the relatively simple eukaryote yeast suggests that complex signalling pathways may be circumvented through the direct interaction between individual metabolites and regulators of RNA polymerase II-mediated transcription. Biochemical and structural analyses are beginning to unravel these elegant genetic control elements.

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