A line search exact penalty method using steering rules
The article of Richard H. Bryd, Gabriel Lopez-Calva and Jorge Nocedal is a valuable contribution to the field of numerical nonlinear optimization - such to say, another milestone in the series of the authors' contributions to this important area of Applied and Industrial Mathematics and Operational Research. This work impresses by the appropriate, elegant and comfortable use and combination of some basic ideas and principles of optimization theory and numerical mathematics, well directed and eventually proven to be successful. As the authors point out, line search algorithms for nonlinear programming must include safeguards to permit global convergence. This article presents an exact penalization approach which extends the class of problems solvable by a line search sequential quadratic programming algorithm. In the new methods, the penalty parameter is adjusted at every iteration to guarantee sufficient progress in the linear feasibility and to promote acceptance of the step. A trust region is assists in the determination of the penalty parameter, however, not in the step computation. It is shown that the algorithm enjoys favorable global convergence properties. Numerical experiments illustrate the behavior of the algorithm on various difficult situations. The mathematically deep and strong article paper is well-written and well-structured. Problems, formulas, algorithms and tables are put with care, meaningful and with success. The five sections of the paper are as follows: 1. Introduction, 2. A line search penalty method, 3. Convergence analysis, 4. Numerical experiments, and 5. Final remarks. In future, further deep methods and results can be expected, prepared and supported by this research paper. These advances can lead to a great progress in the areas of science, engineering, economics, finance, OR, medicine and healthcare and, herewith, to improvements of the living conditions and expectations of the peoples on earth.
scientific article; zbMATH DE number 6050439
scientific article