An efficient simplicial algorithm for computing a zero of a convex union of smooth functions |
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Authors: | Samuel A Awoniyi Michael J Todd |
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Institution: | (1) University of Ibadan, Ibadan, Nigeria;(2) Cornell University, Ithaca, NY, USA |
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Abstract: | We present an efficient simplicial algorithm for computing a zero of a point-to-set mapping that is formed by piecing together
smooth functions. Such mappings arise in nonlinear programming and economic equilibrium problems. Our algorithm, under suitable
regularity conditions on the problem, generates a sequence converging at least Q-superlinearly to a zero of the mapping. Asymptotically,
it operates in a space of reduced dimension, analogous to an active set strategy in the optimization setting, but it switches
active sets automatically. Results of computational experiments are given.
Research of this author was supported by a Fellowship from the Rockeffeller Foundation.
Research of this author was partially supported by a fellowhip from the John Simon Guggenheim Memorial Foundation and by National
Science Foundation Grant ECS-7921279. |
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Keywords: | Simplicial Algorithm Piecewise-linear Homotopy Nonlinear Programming Economic Equilibrium Problems Q-superlinear Convergence |
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