Morse Programs: A Topological Approach to Smooth Constrained Optimization.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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We consider nonlinear constrained optimization problems whose objective and constraint functions are sufficiently smooth. No convexity is assumed. Our basic tools are from differential topology. We show that these problems can be reduced to the study of minimizing a Morse function on a manifold with boundary and we give the geometrical meaning to the first order conditions, the second order sufficiency conditions, and strict complementary slackness condition. Our main concerns are the second order sufficiently conditions, sensitivity analysis, generic properties of smooth nonlinear programs, global duality, local uniqueness, and strict complementary slackness. Author
- Theoretical Mathematics