TY  - JOUR
ID  - iiasa14158
UR  - https://pure.iiasa.ac.at/id/eprint/14158/
IS  - 1-3
A1  - Gilbert, J.C.
N2  - We propose an algorithm for minimizing a functionf on ?n in the presence ofm equality constraintsc that locally is a reduced secant method. The local method is globalized using a nondifferentiable augmented Lagrangian whose decrease is obtained by both a longitudinal search that decreases mainlyf and a transversal search that decreases mainly ?c?. Our main objective is to show that the longitudinal path can be designed to maintain the positive definiteness of the reduced matrices by means of the positivity of?kT?k, where?k is the change in the reduced gradient and ?k is the reduced longitudinal displacement.
VL  - 50
TI  - Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization
AV  - none
EP  - 28
Y1  - 1991///
PB  - Springer
JF  - Mathematical Programming
KW  - Augmented Lagrangian; constrained optimization; exact penalty function; global convergence; optimization algorithm; reduced secant method; superlinear convergence; Wolfe's step-size selection
SN  - 0025-5610
SP  - 1
ER  -