Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.
The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization.The feasibility restoration phase,which is always used in the traditional filter method,is not needed.Under mild conditions,global convergence and local superlinear convergence rates are obtained.Numerical results demonstrate that the new algorithm is effective.
