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Morse Programs

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  • Okitsugu Fujiwara

Abstract

Spingarn and Rockafellar [13] showed in a program (Q_{v}^{u}) minimize {f(x) - u^{T}x subject to g(x) = m; that at any local minimum point x of (Q_{v}^{u}) the Jacobian matrix of g at x has full rank, strict complementary slackness holds and the second order sufficiency conditions hold, for almost every matrix{u v} in R^{n} times R^{m} (Lebesgue measure). The purpose of this paper is to explicate the geometry underlying their work and to exploit this geometry in the generic analysis of constrained optimization problems. Namely we show that their work can be reduced to the study of minimizing a Morse function on a manifold with boundary. We follow a classical tradition of first studying an equality constrained program and then reducing inequality constrained programs to a finite family of equality constrained programs, through the device of active (or binding) constraints.

Suggested Citation

  • Okitsugu Fujiwara, 1979. "Morse Programs," Cowles Foundation Discussion Papers 539, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:539
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d05/d0539.pdf
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    References listed on IDEAS

    as
    1. Araujo, Aloisio & Mas-Colell, Andreu, 1978. "Notes on the smoothing of aggregate demand," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 113-127, September.
    2. Chichilnisky, Graciela & Kalman, Peter J, 1978. "Comparative Statics of Less Neoclassical Agents," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(1), pages 141-148, February.
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