Thursday, 14:15 - 14:40 h, Room: H 0110


Luiz-Rafael Santos
A polynomial optimization subproblem in interior-point methods

Coauthors: Aurelio Oliveira, Clovis Perin, Fernando Villas-Bôas


In this work we study a primal-dual path-following interior point method for linear programming. Our approach, based on Mehrotra's predictor-corrector methods, combines three types of directions to generate a better one by making an extensive use of real-valued polynomials on variables ( α,\mu,σ), where α is the step length, \mu defines a more general central path, and σ models the weight that a predictor direction should have. We develop a merit function that is a polynomial in ( α,\mu,σ) and that is used as a guide to combine those directions. This merit function is subjected to polynomial constraints, which are designed to keep the next point into a good neighbourhood of the central path - a generalization of Gondzio-Colombo's symmetric neighbourhood. A polynomial optimization problem (POP) arises from this approach and its global solution, in each iteration, leads to the choice of the next direction. Different methods for solving the POP are being experimented and the computational experiments are promising.


Talk 3 of the contributed session Thu.2.H 0110
"Interior-point methods for linear programming" [...]
Cluster 16
"Nonlinear programming" [...]


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