Open AccessJournal Article
A logarithmic barrier function method for solving nonlinear multiobjective programming problems
M. Tlas,B. Abdul Ghani +1 more
TL;DR: An interior point method for solving nonlinear objective programming problems, over a convex set contained in the real space R n, has been developed in this paper, where a new strictly concave logarithmic barrier function has been fused in order to transform the orginal problem into a sequence of unconstrained subproblems.
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Abstract: An interior point method for solving nonlinear mul- tiobjective programming problems, over a convex set contained in the real space R n , has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been sug- gested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved us- ing Newton method for determining Newton's directions along which line searches are performed. It also has been proved that the number of iterations required by the suggested algorithm to converge to an "-optimal solution is O(m |ln"|), depending on predetermined error tolerance " and the number of constraints m.
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Citations
Nonlinear Multiobjective Programming
Alexander Engau
- 15 Feb 2011
TL;DR: This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems.
10
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