Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions

Jin-Bao Jian, Chun-Ming Tang and Hai-Yan Zheng

European Journal of Operational Research, 2010, vol. 200, issue 3, 645-657

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.

Keywords: Optimization; Quadratically; constrained; quadratic; programming; SQCQP; superlinear; convergence; Norm-relaxed; algorithm (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:200:y:2010:i:3:p:645-657

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