Nonlinear Programming: Sequential Unconstrained Minimization TechniquesRecent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them. |
Other editions - View all
Nonlinear Programming: Sequential Unconstrained Minimization Techniques Anthony V. Fiacco,Garth P. McCormick No preview available - 1990 |
Common terms and phrases
additional algorithm analysis applied approach approximation assumed assumptions boundary bounded Chapter Clearly compact computational Consider constraint qualification constraints contained continuous convergence convex function convex programming problem Corollary corresponding decreasing defined differentiable direction discussed dual equality equations example exists exterior fact finite first first-order follows give given global gradient hence hold implies independent indicated inequality interesting interior point inverse isolated iteration Lagrangian Lemma limit point linear local minimum logarithmic matrix method minimum modified multipliers necessary conditions nonlinear programming Note objective function obtained optimal optimum particular penalty function point algorithms positive definite possible problem functions procedure Proof properties proved quadratic respect satisfied satisfying second partial derivatives second-order sequence solution solve starting steps strictly sufficient technique term Theorem theory trajectory unconstrained function unconstrained minimization unique variables vector yields zero