Abstract
In constrained optimization problems in mathematical programming, one wants to minimize a functionalf(x) over a given setC. If, at an approximate solutionx n , one replacesf(x) by its Taylor series expansion through quadratic terms atx n and denotes byx n+1 the minimizing point for this overC, one has a direct analogue of Newton's method. The local convergence of this has been previously analyzed; here, we give global convergence results for this and the similar algorithm in which the constraint setC is also linearized at each step.
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Communicated by M. R. Hestenes
This research was supported in part by the Office of Naval Research, Contract No. N00014-67-0126-0015, and was presented by invitation at the Fifth Gatlinburg Symposium on Numerical Algebra, Los Alamos, New Mexico, 1972.
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Daniel, J.W. Global convergence for Newton methods in mathematical programming. J Optim Theory Appl 12, 233–241 (1973). https://doi.org/10.1007/BF00935105
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DOI: https://doi.org/10.1007/BF00935105