Tuesday, 16:15 - 16:40 h, Room: H 0107

 

Mouna Hassan
The l1- Penalty Interior Point Method

Coauthors: Javier Moguerza, Andrés Redchuk

 

Abstract:
The problem of general nonconvex, nonlinear constraint optimization is
addressed, without assuming regularity conditions on the constraints,
and the problem can be degenerate. We reformulate the problem by
applying l1-exact penalty function with shift variables to relax and
regularize the problem. Then a feasible type line search primal-dual
interior point method, approximately solve a sequence of inequality
constraint penalty-barrier subproblems. To solve each subproblems, a
Cauchy step would be computed beside to Newton step and the proposed
algorithm would move along a direction in the span of these two
steps. The penalty parameter is checked at the end of each iteration
as we do with the barrier parameter, since we do not need to update
the penalty parameter before performing the line search. If the multipliers are finite, then the corresponding penalty parameter is finite. Global convergence properties do not require the regularity conditions on the original problem. The solution to the penalty-barrier problem converge to the optima that may satisfy the Karush-Kuhn-Tuker point or Fritz-John point, and may satisfy a first-order critical point for the measure of the

 

Talk 3 of the contributed session Tue.3.H 0107
"Interior-point methods" [...]
Cluster 16
"Nonlinear programming" [...]

 

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