A quadratically approximate framework for constrained optimization, global and local convergence

作者：Jian; Jin Bao

来源：Acta Mathematica Sinica-English Series, 2008, 24(5): 771-788.

DOI：10.1007/s10114-007-4465-0

• constrained optimization
• quadratic approximation
• algorithm framework
• quadratic constraints
• global and local convergence

This paper presents a quadratically approximate algorithm framework (QAAF) for solving general constrained optimization problems, which solves, at each iteration, a subproblem with quadratic objective function and quadratic equality together with inequality constraints. The global convergence of the algorithm framework is presented under the Mangasarian-Fromovitz constraint qualification (MFCQ), and the conditions for superlinear and quadratic convergence of the algorithm framework are given under the MFCQ, the constant rank constraint qualification (CRCQ) as well as the strong second-order sufficiency conditions (SSOSC). As an incidental result, the definition of an approximate KKT point is brought forward, and the global convergence of a sequence of approximate KKT points is analysed.

• 出版日期2008-5
• 单位广西大学