Abstract
This note extends the fundamental theorems of Morse theory for stable stationary solutions to optimization problems on manifolds with corners.
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MILNOR, J., Morse Theory, Annals of Mathematics Studies, Princeton University Press, Princeton, New Jersey, Vol. 51, 1963.
JONGEN, H. T., JONKER, P., and TWILT, F., Nonlinear Optimization in R n , I: Morse Theory, Chebychev Approximation, Peter Lang Verlag, Frankfurt, Germany, 1983.
GUDDAT, J., JONGEN, H. T., and RÜCKMANN, J., On Stability and Stationary Points in Nonlinear Optimization, Journal of Australian Mathematical Society, Vol. 28B, pp. 36-56, 1986.
AGRACHEV, A. A., and VAKHRAMEEV, S. A., Morse Theory and Optimal Control Problems, Nonlinear Synthesis, Sopron, Hungary, 1989; Progress in Systems Control Theory, Birkhäuser Boston, Boston, Massachusetts, Vol. 9, pp. 1-11, 1991.
KOJIMA, M., Strongly Stable Stationary Solutions in Nonlinear Programs, Analysis and Computation of Fixed Points, Edited by S. M. Robinson, Academic Press, New York, NY, pp. 93-138, 1980.
HIRABAYASHI, R., JONGEN, H. T., and SHIDA, M., Stability for Linearly Constrained Optimization Problems, Mathematical Programming, Vol. 66, pp. 351-360, 1994.
HIRSCH, M. W., Differential Topology, Graduate Texts in Mathematics, Springer Verlag, Berlin, Germany, Vol. 33, 1976.
PALAIS, R. S., and SMALE, S., A Generalized Morse Theory, Bulletin of the American Mathematical Society, Vol. 70, pp. 165-172, 1964.
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Shida, M. Fundamental Theorems of Morse Theory for Optimization on Manifolds with Corners. Journal of Optimization Theory and Applications 106, 683–688 (2000). https://doi.org/10.1023/A:1004669815654
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DOI: https://doi.org/10.1023/A:1004669815654