A superlinearly convergent strongly sub-feasible SSLE-type algorithm with working set for nonlinearly constrained optimization
The following nonlinear inequality constrained optimization problem is considered: \[ \text{Minimize }f(x)\text{ subject to }g_i(x)\leq 0,\;i=1, \dots, m, \] where \(f:\mathbb{R}^n\to \mathbb{R}\), \(g_i:\mathbb{R}^n\to \mathbb{R}\) for all \(i=1,\dots,m\) are continuously differentiable functions. Using a new identification technique of active constraints and the method of strongly sub-feasible directions, the authors develop a new algorithm based on a sequential system of linear equations. The algorithm can be started from an arbitrary initial point. After a finite number of iterations, the algorithm generates a feasible iteration point and continues its work as the known method of feasible directions. Global, strong and superlinear convergence of the proposed algorithm are proved. Experimental numerical results in the concluding part of the paper show the effectiveness of the algorithm.
scientific article; zbMATH DE number 5522048
scientific article