Abstract. We propose a trust region-line search projected exact penalty algorithm for solving constrained nonlinear optimization problems (NLPs). We make use of the well-known relationship between the solutions of NLP and the minimizers of the -exact penalty function to design the algorithm. In our algorithm, whenever the current iterate is far from the feasible region, either a potential infeasible stationary 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 using 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 horizontal 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 Lagrange 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 methods. We also demonstrate a two-step superlinear local rate of convergence of the algorithm. We implement the algorithm in the MATLAB environment. Comparative numerical experiments on some test problems from the CUTEst library confirm the competitiveness of the proposed algorithm in comparison with a number of well-developed NLP solvers.
How to Cite this Article:
H. Ahmadzadeh, N. Mahdavi-Amiri, Convergence analysis and competitive numerical results of a trust region-line search projected exact penalty algorithm, J. Nonlinear Var. Anal. 10 (2026), 435-470.
