Convergence Conditions for Ascent Methods

Abstract

Previous article Next article Convergence Conditions for Ascent MethodsPhilip WolfePhilip Wolfehttps://doi.org/10.1137/1011036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractLiberal conditions on the steps of a “descent” method for finding extrema of a function are given; most known results are special cases.[1] Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261 MR0010667 0061.26801 CrossrefGoogle Scholar[2] Augustine Cauchy, Méthode générale pour la résolution des systèmes d'équations simultanées, C.R. Acad. Sci., 25 (1847), 536–538 Google Scholar[3] A. A. Goldstein, Minimizing functionals on normed-linear spaces, SIAM J. Control, 4 (1966), 81–89 10.1137/0304008 MR0196900 0147.12701 LinkGoogle Scholar[4] A. A. Goldstein, Cauchy's method of minimization, Numer. Math., 4 (1962), 146–150 10.1007/BF01386306 MR0141222 0105.10201 CrossrefGoogle Scholar[5] Alexander Ostrowski, Solution of equations and systems of equations, Second edition. Pure and Applied Mathematics, Vol. 9, Academic Press, New York, 1966xiv+338 MR0216746 0222.65070 Google Scholar[6] G. Zoutehdijk, 1967, Private communication Google Scholar[7] R. Fletcher and , C. M. Reeves, Function minimization by conjugate gradients, Comput. J., 7 (1964), 149–154 10.1093/comjnl/7.2.149 MR0187375 0132.11701 CrossrefISIGoogle Scholar[8] W. Oettli, 1967, Private communication Google Scholar[9] L. V. Kantorovich and , G. P. Akilov, Functional analysis in normed spaces, Translated from the Russian by D. E. Brown. Edited by A. P. Robertson. International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Co., New York, 1964xiii+771, Chap. 15 MR0213845 0127.06104 Google Scholar[10] Hirotugu Akaike, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method, Ann. Inst. Statist. Math. Tokyo, 11 (1959), 1–16 10.1007/BF01831719 MR0107973 0100.14002 CrossrefISIGoogle Scholar[11] R. Fletcher and , M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J., 6 (1963/1964), 163–168 MR0152116 0132.11603 CrossrefISIGoogle Scholar[12] M. J. Box, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J., 9 (1966), 67–77 MR0192645 0146.13304 CrossrefISIGoogle Scholar[13] Donald M. Topkis and , Arthur F. Veinott, on the convergence of some feasible direction algorithms for nonlinear programming, J. SIAM control, 5 (1967), 268–274 10.1137/0305018 0158.18805 LinkGoogle Scholar[14] Philip Wolfe, on the convergence of gradient methods under constraints, Rep., RZ-204, IBM watson research center, yorktown heights, new york, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Two efficient modifications of AZPRP conjugate gradient method with sufficient descent propertyJournal of Inequalities and Applications, Vol. 2022, No. 1 | 10 January 2022 Cross Ref Optimal Transport Based Seismic Inversion:Beyond Cycle SkippingCommunications on Pure and Applied Mathematics, Vol. 75, No. 10 | 1 April 2021 Cross Ref A robust BFGS algorithm for unconstrained nonlinear optimization problemsOptimization, Vol. 17 | 19 September 2022 Cross Ref Two Methods for the Implicit Integration of Stiff Reaction SystemsComputational Methods in Applied Mathematics, Vol. 0, No. 0 | 14 September 2022 Cross Ref Simple and fast convergent procedure to estimate recursive path analysis modelBehaviormetrika, Vol. 107 | 6 September 2022 Cross Ref Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functionsNumerical Algorithms, Vol. 91, No. 1 | 20 January 2022 Cross Ref A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization ProblemsMathematics, Vol. 10, No. 17 | 23 August 2022 Cross Ref Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamicsBIT Numerical Mathematics, Vol. 48 | 11 August 2022 Cross Ref An outlier-resistant κ -generalized approach for robust physical parameter estimationPhysica A: Statistical Mechanics and its Applications, Vol. 600 | 1 Aug 2022 Cross Ref An Active Set Trust-Region Method for Bound-Constrained OptimizationBulletin of the Iranian Mathematical Society, Vol. 48, No. 4 | 27 July 2021 Cross Ref Advancing Three-Dimensional Coupled Water Quality Model of Marine Ranches: Model Development, Global Sensitivity Analysis, and Optimization Based on Observation SystemJournal of Marine Science and Engineering, Vol. 10, No. 8 | 27 July 2022 Cross Ref Robust regression against heavy heterogeneous contaminationMetrika, Vol. 16 | 1 July 2022 Cross Ref A new class of nonlinear conjugate gradient coefficients for unconstrained optimizationAsian-European Journal of Mathematics, Vol. 15, No. 07 | 14 October 2021 Cross Ref New iterative conjugate gradient method for nonlinear unconstrained optimizationRAIRO - Operations Research, Vol. 56, No. 4 | 29 July 2022 Cross Ref Optimizing Oblique Projections for Nonlinear Systems using TrajectoriesSamuel E. 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