Abstract
With the aim of providing new algorithmic tools for assuring good, global convergence properties for methods solving convex programming problems, we present some results and proposals concerning: 1.) a new, homotopy method for solving linear (convex, analytic) programming problems; 2.) global rational extrapolation (approximation) as a tool (combined with suitable analytic homotopies) for path following (e.g. solving analytic systems equations for saddle points). While introducing these tools we emphasize the importance of the use of “global” and “analytic” tools (in contrast to the use of “local” notions and “nondifferentiable” objects): from this (rather general) perspective a linear (convex, analytic) programming problem should be regarded as a “nondifferentiable” one only if the number of constraints is much higher than the number of variables.
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Abbreviations
- for running heads:
-
New methods in convex programming.
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© 1988 Birkhaürser Verlag Basel
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Sonnevend, G. (1988). New Algorithms in Convex Programming Based on a Notion of “Centre” (for Systems of Analytic Inequalities) and on Rational Extrapolation. In: Hoffmann, KH., Zowe, J., Hiriart-Urruty, JB., Lemarechal, C. (eds) Trends in Mathematical Optimization. International Series of Numerical Mathematics/Internationale Schriftenreihe zur Numerischen Mathematik/Série internationale d’Analyse numérique, vol 84. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9297-1_20
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DOI: https://doi.org/10.1007/978-3-0348-9297-1_20
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