Abstract
This paper investigates some convergence properties of Fiacco and McCormick's SUMT algorithm. A convex programming problem is given for which the SUMT algorithm generates a unique unconstrained minimizing trajectory having an infinite number of accumulation points, each a global minimizer to the original convex programming problem.
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References
A.V. Fiacco and G.P. McCormick, “The sequential unconstrained minimization technique for nonlinear programming, a primal-dual method”,Management Science 10 (1964) 360–366.
A.V. Fiacco and G.P. McCormick, “Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming”,Management Science 10 (1964) 601–617.
A.C. Fiacco and G.P. McCormick,Nonlinear programming: Sequential unconstrained minimization techniques (Wiley, New York, 1968).
C.L. Sandblom, “On the convergence of SUMT”, National Economic Planning Research Papers RC/A 64, University of Birmingham, Great Britain (1972).
P. Wolfe, “Convergence theory in nonlinear programming”, in:Integer and nonlinear programming Ed. J. Abadie (North-Holland, Amsterdam, 1970) pp. 1–36.
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Sandblom, CL. On the convergence of SUMT. Mathematical Programming 6, 360–364 (1974). https://doi.org/10.1007/BF01580251
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DOI: https://doi.org/10.1007/BF01580251