Convergence analysis and competitive numerical results of a trust region-line search projected exact penalty algorithm

We propose a trust region-line search projected exact penalty algorithm for solving con- strained nonlinear optimization problems (NLPs). We make use of the well-known relationship between the solutions of NLP and the minimizers of the ℓ1-exact penalty function to design the algorithm. In our algorithm, whenever the current iterate is far from the feasible region, either a potential infeasible station- ary point is identified, or the penalty parameter is decreased to navigate the iterates towards the feasible region. After updating the penalty parameter, a descent direction for the penalty function is computed us- ing an approximate minimizer of a projected quadratic model of the penalty function over a trust region. In nearly feasible or feasible iterations, the step direction is determined by a combination of a horizon- tal step and a vertical step directions. The horizontal step direction is computed to reduce the penalty function, while the vertical step direction is calculated to preserve feasibility. Near stationarity, the La- grange multipliers are computed by solving a linear least squares problem. If the computed Lagrange multipliers satisfy the first-order optimality conditions, a Newton step direction is computed to obtain a fast rate of convergence to a first-order point of NLP. Otherwise, a dropping step is calculated to decrease the penalty function value. The step length along the dropping step is computed using a backtracking line search strategy. We use the BFGS updating formula to update the approximate projected Hessian in local iterations. Here, we establish the global convergence of the proposed trust region-line search algorithm under conditions less stringent than those required by other available exact penalty