Popov, L. D. Quadratic approximation of penalty functions for solving large-scale linear programs. (Russian, English) Zbl 1210.49034 Zh. Vychisl. Mat. Mat. Fiz. 47, No. 2, 206-221 (2007); translation in Comput. Math. Math. Phys. 47, No. 2, 200-214 (2007). Summary: Using the least squares, modified Lagrange function, and some other methods as examples, the capabilities of the new optimization technique based on the quadratic approximation of penalty functions that has been recently proposed by O. Mangasarian for a special class of linear programming problems are demonstrated. The application of this technique makes it possible to use unified matrix operations and standard linear algebra packages (including parallel ones) for solving large-scale problems with sparse strongly structured constraint matrices. With this technique, the computational schemes of some well-known algorithms can take an unexpected form. Cited in 5 Documents MSC: 49M30 Other numerical methods in calculus of variations (MSC2010) Keywords:large scale linear programming; generalized Newton method; Lagrange function Software:OOPS PDFBibTeX XMLCite \textit{L. D. Popov}, Zh. Vychisl. Mat. Mat. Fiz. 47, No. 2, 206--221 (2007; Zbl 1210.49034); translation in Comput. Math. Math. Phys. 47, No. 2, 200--214 (2007) Full Text: DOI