A logarithmic barrier cutting plane method for convex programming

1995 ◽  
Vol 58 (2) ◽  
pp. 67-98 ◽  
Author(s):  
D. den Hertog ◽  
J. Kaliski ◽  
C. Roos ◽  
T. Terlaky
Keyword(s):  
Convex Programming ◽  
Cutting Plane ◽  
Cutting Plane Method ◽  
Plane Method ◽  
Logarithmic Barrier

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

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

2021 ◽  
Vol 1 ◽  
pp. 30-40
Author(s):  
Natalia V. Semenova ◽  
◽  
Maria M. Lomaga ◽  
Viktor V. Semenov ◽  
◽  
...  
Keyword(s):  
System Optimization ◽  
Cutting Plane ◽  
Recession Cone ◽  
Cutting Plane Method ◽  
Optimal Solutions ◽  
Feasible Set ◽  
Plane Method ◽  
Multicriteria Problems ◽  
Lexicographic Optimization ◽  
Feasible Solutions

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

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