An Evolutionary Analytic Center Classifier

2020 ◽  
pp. 34-48
Author(s):  
Renan Motta Goulart ◽  
Saulo Moraes Villela ◽  
Carlos Cristiano Hasenclever Borges ◽  
Raul Fonseca Neto
Keyword(s):  
Analytic Center

Multiple Cuts in the Analytic Center Cutting Plane Method

2000 ◽  
Vol 11 (1) ◽  
pp. 266-288 ◽  
Author(s):  
Jean-Louis Goffin ◽  
Jean-Philippe Vial
Keyword(s):  
Cutting Plane ◽  
Cutting Plane Method ◽  
Analytic Center ◽  
Plane Method

scholarly journals Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis

2020 ◽  
Vol 48 (4) ◽  
pp. 633-659
Author(s):  
Daniel Bankmann ◽  
Volker Mehrmann ◽  
Yurii Nesterov ◽  
Paul Van Dooren
Keyword(s):  
Discrete Time ◽  
Transfer Functions ◽  
Convex Set ◽  
Solution Set ◽  
Linear Matrix ◽  
Analytic Center ◽  
Matrix Equations ◽  
Matrix Inequalities ◽  
Discrete Time Systems ◽  
Time Systems

AbstractIn this paper formulas are derived for the analytic center of the solution set of linear matrix inequalities (LMIs) defining passive transfer functions. The algebraic Riccati equations that are usually associated with such systems are related to boundary points of the convex set defined by the solution set of the LMI. It is shown that the analytic center is described by closely related matrix equations, and their properties are analyzed for continuous- and discrete-time systems. Numerical methods are derived to solve these equations via steepest descent and Newton methods. It is also shown that the analytic center has nice robustness properties when it is used to represent passive systems. The results are illustrated by numerical examples.

Shallow, deep and very deep cuts in the analytic center cutting plane method

1999 ◽  
Vol 84 (1) ◽  
pp. 89-103 ◽  
Author(s):  
Jean-Louis Goffin ◽  
Jean-Philippe Vial
Keyword(s):  
Cutting Plane ◽  
Cutting Plane Method ◽  
Analytic Center ◽  
Plane Method ◽  
Deep Cuts

An analytic center quadratic cut method for the convex quadratic feasibility problem

2002 ◽  
Vol 93 (2) ◽  
pp. 305-325 ◽  
Author(s):  
Faranak Sharifi Mokhtarian ◽  
Jean-Louis Goffin
Keyword(s):  
Feasibility Problem ◽  
Analytic Center ◽  
Cut Method
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