ABSTRACT: In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the
method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable
for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with
superlinear convergence rate.
The local algorithm is globalized by means of a suitable merit function which is able to measure and to enforce progress of
the iterates towards a KKT pair, without deteriorating the local efficiency. In particular, we adopt the exact augmented Lagrangian
function introduced in Pillo and Lucidi (SIAM J. Optim. 12:376–406, 2001), which allows us to guarantee the boundedness of the sequence produced by the algorithm and which has strong connections
with the above mentioned truncated direction.
The resulting overall algorithm is globally and superlinearly convergent under mild assumptions.
KeywordsConstrained optimization-Nonlinear programming algorithms-Large scale optimization-Truncated Newton-type algorithms-Exact augmented Lagrangian functions
Computational Optimization and Applications 04/2012; 45(2):311-352. · 1.35 Impact Factor
Optimization Letters. 01/2011; 5:347-362.
ABSTRACT: This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond exactly to KKT pairs, local solutions and global solutions of the constrained problem.
Computational Optimization and Applications 03/2003; 25(1):57-83. · 1.35 Impact Factor