An Interior Point Algorithm for Large-Scale Nonlinear Programming

The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.

[1]  M. J. D. Powell,et al.  Nonlinear Programming—Sequential Unconstrained Minimization Techniques , 1969 .

[2]  N. Maratos,et al.  Exact penalty function algorithms for finite dimensional and control optimization problems , 1978 .

[3]  Johannes Jahn,et al.  An interior point method for nonlinear programming , 1979, Z. Oper. Research.

[4]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

[5]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[6]  Philip E. Gill,et al.  Practical optimization , 1981 .

[7]  C. Lemaréchal,et al.  The watchdog technique for forcing convergence in algorithms for constrained optimization , 1982 .

[8]  T. Steihaug.  The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[9]  Richard A. Tapia,et al.  A trust region strategy for nonlinear equality constrained op-timization , 1984 .

[10]  T. Coleman,et al.  On the Local Convergence of a Quasi-Newton Method for the Nonlinear Programming Problem , 1984 .

[11]  A. Vardi.  A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation , 1985 .

[12]  Richard H. Byrd,et al.  A Trust Region Algorithm for Nonlinearly Constrained Optimization , 1987 .

[13]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[14]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[15]  E. Omojokun.  Trust region algorithms for optimization with nonlinear equality and inequality constraints , 1990 .

[16]  P. Toint,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[17]  T. Coleman,et al.  On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds , 1992 .

[18]  P. Toint,et al.  A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization , 1994 .

[19]  K. Anstreicher,et al.  On the convergence of an infeasible primal-dual interior-point method for convex programming , 1994 .

[20]  T. Plantenga.  Large-scale nonlinear constrained optimization using trust regions , 1994 .

[21]  Florian,et al.  On the Role of the Objective Function in BarrierMethods , 1994 .

[22]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[23]  Margaret H. Wright,et al.  Why a Pure Primal Newton Barrier Step May be Infeasible , 1995, SIAM J. Optim..

[24]  Nicholas I. M. Gould,et al.  CUTE: constrained and unconstrained testing environment , 1995, TOMS.

[25]  L. N. Vicente,et al.  Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming Problems , 1998 .

[26]  Hiroshi Yamashita,et al.  Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization , 1996, Math. Program..

[27]  T. Tsuchiya,et al.  On the formulation and theory of the Newton interior-point method for nonlinear programming , 1996 .

[28]  Jorge Nocedal,et al.  Large-scale constrained optimization , 1996 .

[29]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[30]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[31]  M. Ramos.  Exact and inexact Newton linesearch interior-point algorithms for nonlinear programming problems , 1997 .

[32]  Zefferino Paroda Garcia.  A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual quasi-Newton interior-point method for nonlinear programming , 1997 .

[33]  J. Frédéric Bonnans,et al.  A Trust Region Interior Point Algorithm for Linearly Constrained Optimization , 1997, SIAM J. Optim..

[34]  Jorge Nocedal,et al.  On the Local Behavior of an Interior Point Method for Nonlinear Programming , 1997 .

[35]  Hiroshi Yamashita.  A globally convergent primal-dual interior point method for constrained optimization , 1998 .

[36]  Jorge Nocedal,et al.  On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization , 1998, SIAM J. Optim..

[37]  Yanhui Wang,et al.  Trust region affine scaling algorithms for linearly constrained convex and concave programs , 1998, Math. Program..

[38]  Michael L. Overton,et al.  A Primal-dual Interior Method for Nonconvex Nonlinear Programming , 1998 .

[39]  Todd Plantenga,et al.  A Trust Region Method for Nonlinear Programming Based on Primal Interior-Point Techniques , 1998, SIAM J. Sci. Comput..

[40]  Anders Forsgren,et al.  Primal-Dual Interior Methods for Nonconvex Nonlinear Programming , 1998, SIAM J. Optim..

[41]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[42]  Thomas de Quincey.  [C] , 2000, The Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820.

[43]  P. Toint,et al.  A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints , 2000 .