An Interior-point algorithm with a line-search globalization is proposed for solving the general nonlinear programming problem. At each iteration, the search direction is obtained as a resultant of two orthogonal vectors. They are obtained by solving two square linear systems. An upper-triangular linear system is solved to obtain the Lagrange multiplier vector. The three systems that must be solved each iteration are reduced systems obtained using the projected Hessian technique. This fits well for large-scale problems. A modified Hessian technique is embedded to provide a sufficient descent for the search direction. Then the length of the direction is decided by backtracking line search with the use of a merit function to generate an acceptable next point. |
