Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions |
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Authors: | Jin-Bao Jian Chun-Ming Tang Hai-Yan Zheng |
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Institution: | aCollege of Mathematics and Information Science, Guangxi University, 530004 Nanning, PR China |
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Abstract: | In this paper, we present a sequential quadratically constrained quadratic programming (SQCQP) norm-relaxed algorithm of strongly sub-feasible directions for the solution of inequality constrained optimization problems. By introducing a new unified line search and making use of the idea of strongly sub-feasible direction method, the proposed algorithm can well combine the phase of finding a feasible point (by finite iterations) and the phase of a feasible descent norm-relaxed SQCQP algorithm. Moreover, the former phase can preserve the “sub-feasibility” of the current iteration, and control the increase of the objective function. At each iteration, only a consistent convex quadratically constrained quadratic programming problem needs to be solved to obtain a search direction. Without any other correctional directions, the global, superlinear and a certain quadratic convergence (which is between 1-step and 2-step quadratic convergence) properties are proved under reasonable assumptions. Finally, some preliminary numerical results show that the proposed algorithm is also encouraging. |
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Keywords: | Optimization Quadratically constrained quadratic programming SQCQP superlinear convergence Norm-relaxed algorithm |
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