This paper presents a quadratically converging algorithm for unconstrained minimization. All the accumulation points that it constructs satisfy second-order necessary conditions of optimality. Thus, it avoids second-order saddle andinflection points, an essential feature for a method to be used in minimizing the modified Lagrangians in multiplier methods.
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The work of the first author was supported by NSF RANN AEN 73-07732-A02 and JSEP Contract No. F44620-71-C-0087; the work of the second author was supported by NSF Grant No. GK-37672 and the ARO Contract No. DAHCO4-730C-0025.
Communicated by D. Q. Mayne
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Mukai, H., Polak, E. A second-order method for unconstrained optimization. J Optim Theory Appl 26, 501–513 (1978). https://doi.org/10.1007/BF00933149
- Unconstrained optimization
- quadratic convergence
- second-order conditions