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Jacobian nonsingularity in nonlinear symmetric conic programming problems and its application. (English) Zbl 1459.90203

Summary: This paper considers the nonlinear symmetric conic programming (NSCP) problems. Firstly, a type of strong sufficient optimality condition for NSCP problems in terms of a linear-quadratic term is introduced. Then, a sufficient condition of the nonsingularity of Clarke’s generalized Jacobian of the Karush-Kuhn-Tucker (KKT) system is demonstrated. At last, as an application, this property is used to obtain the local convergence properties of a sequential quadratic programming- (SQP-) type method.

MSC:

90C30 Nonlinear programming
90C31 Sensitivity, stability, parametric optimization
49J52 Nonsmooth analysis
90C46 Optimality conditions and duality in mathematical programming
90C55 Methods of successive quadratic programming type
90C22 Semidefinite programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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