Two New Strongly Sub-feasible And Quasi-strongly Sub-feasible Algorithms For Inequality Constrained Optimization

In this thesis, the nonlinear optimization problems with inequality constraints are dis-cussed. In Chapter 1, combining the method of strongly sub-feasible directions (MSSFD)and theε- generalized projection technique, a new algorithm starting with an arbitraryinitial iteration point for the discussed problems is proposed. At each iteration, the searchdirection is generated by a newε-generalized projection explicit formula, and the step lengthis yielded by a new Armijo line search.In Chapter 2, the aim is to further improve the algorithm in Chapter 1. Combiningthe method of quasi-strongly sub-feasible directions (MQSSFD) and the working set tech-nique, we present a new sequential systems of linear equations (SSLE) algorithm startingwith an arbitrary initial iteration point. At each iteration, the algorithm solves only two sys-tems of linear equations with a same uniformly nonsingular coe?cient matrix to obtain thesearch direction. Particularly, the positive definiteness assumption on the Hessian estimateis relaxed.Under some necessary assumptions, the two new algorithms not only possesse globaland strong convergence, but also the iteration points always get into the feasible set afterfinite iterations. Finally, some preliminary numerical results are reported to show that thealgorithms are promising and e?ective.