Geodesic
On a Second-Order Step-Size Algorithm
Yugoslav journal of operations research, Tome 12 (2002) no. 1, p. 121 .

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In this paper we present a modification of the second-order step-size algorithm. This modification is based on the so called forcing functions. It is proved that this modified algorithm is well-defined. It is also proved that every point of accumulation of the sequence generated by this algorithm is a second-order point of the nonlinear programming problem. Two different convergence proofs are given having in mind two interpretations of the presented algorithm.
Keywords: Forcing function, step-size algorithm, second-order conditions. 
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Nada I. Djuranović-Miličić. On a Second-Order Step-Size Algorithm. Yugoslav journal of operations research, Tome 12 (2002) no. 1, p. 121 . http://geodesic.mathdoc.fr/item/YJOR_2002_12_1_a8/