Research On New SQCQP Algorithms For Inequality Constrained Optimization

Inequality constrained optimization is one of the most important branch-es in the field of mathematical programming, which is widely applied in prac-tical problems, such as economic plan, power network planning, real-time control, engineering design, transportation and so on. The focus of the in-equality constrained optimization research is to explore and design all kinds of quick, effective and practical numerical optimization methods. The the-sis studies new numerical algorithms for solving inequality constrained op-timization problems by means of the ideas of sequential quadratically con-strained quadratic programming (SQCQP) method, penalty function method and an accurate identification technology of active set.Firstly, a new penalty-function type globally convergent SQCQP algo-rithm for inequality constrained optimization problems is proposed. The al-gorithm can choose an initial iteration point arbitrarily, at each iteration only a convex quadratically constrained quadratic programming (QCQP) subprob-lem which always has an optimal solution needs to be solved and the scale of the subproblems and computational cost are reduced by employing the active set accurately identification technology. Without conditions such as the con-vexity of functions and Slater constraint qualification, global convergence of the algorithm is proved. In addition, the algorithm is stable and effective in the process of numerical tests. Secondly, a new fast convergent SQCQP algorithm is established. By constructing a new QCQP subproblem and designing a appropriate penal-ty parameter correction strategy as well as a new line search, the presented algorithm is not only able to begin with an arbitrary initial point, but also guarantees that all of the iterates are turned into feasible ones after a finite number of iterations. And without the linearly independent constraint quali-fication (LICQ) or the strict complementarity, the weakly global, global and superlinear convergence properties are obtained under relatively milder con-ditions. Lastly, the validity of the algorithm is tested through a certain scale of numerical experiments.