作者:
Yamakawa, YuyaOkuno, TakayukiKyoto Univ
Grad Sch Informat Dept Appl Math & Phys Sakyo Ku Yoshida Honmachi Kyoto 6068501 Japan Seikei Univ
Fac Sci & Technol Kichijouji 1-3-1 Musashino Tokyo 1808633 Japan RIKEN
Ctr Adv Intelligence Project Chuo Ku Nihonbashi 1 Chome Mitsui Bldg15th Floor Tokyo 1030027 Japan
In this paper, we propose a new sequentialquadraticsemidefiniteprogramming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence o...
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In this paper, we propose a new sequentialquadraticsemidefiniteprogramming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilizedquadraticsemidefiniteprogramming (QSDP) subproblems, which we derive from the minimax problem associated with the NSDP. Unlike the existing SQSDP methods, the proposed one allows us to solve those QSDP subproblems inexactly, and each QSDP is feasible. One more remarkable point of the proposed method is that constraint qualifications or boundedness of Lagrange multiplier sequences are not required in the global convergence analysis. Specifically, without assuming such conditions, we prove the global convergence to a point satisfying any of the following: the stationary conditions for the feasibility problem, the approximate-Karush-Kuhn-Tucker (AKKT) conditions, and the trace-AKKT conditions. Finally, we conduct some numerical experiments to examine the efficiency of the proposed method.
The stabilizedsequentialquadraticprogramming (SQP) method can effectively deal with degenerate nonlinear optimization problems. In the case of nonunique Lagrange multipliers associated with a stationary point of an...
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The stabilizedsequentialquadraticprogramming (SQP) method can effectively deal with degenerate nonlinear optimization problems. In the case of nonunique Lagrange multipliers associated with a stationary point of an optimization problem, the stabilized SQP method still obtains superlinear and/or quadratic convergence to a primal-dual solution. In this paper, we propose a stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefiniteprogramming problems. Under the local error bound condition, the strict complementarity condition, and the second-order sufficient condition, we establish superlinear and/or quadratic convergence of the proposed method.
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