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The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications

Department of Mathematics, National University of Singapore, Republic of Singapore
matsundf{at}nus.edu.sg, http://www.math.nus.edu.sg/matsundf/

For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson’s constraint qualification, the following conditions are proved to be equivalent: the strong second-order sufficient condition and constraint nondegeneracy; the nonsingularity of Clarke’s Jacobian of the Karush-Kuhn-Tucker system; the strong regularity of the Karush-Kuhn-Tucker point; and others.

Key Words: nonlinear semidefinite programming; strong second-order sufficient condition; constraint nondegeneracy; strong regularity
History: Received: May 16, 2005; revision received: November 21, 2005;

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