A new augmented Lagrangian function for inequality constraints in nonlinear programming problems

Rockafellar, R. T.,Penalty Methods and Augmented Lagrangians in Nonlinear Programming, 5th IFIP Conference on Optimization Techniques, Part 1, Edited by R. Conti and A. Ruberti, Springer-Verlag, Berlin, Germany, 1973.

Fletcher, R.,Methods Related to Lagrangian Functions, Numerical Methods for Constrained Optimization, Edited by P. E. Gill and W. Murray, Academic Press, New York, New York, 1974.

Pierre, D. A., andLowe, M. J.,Mathematical Programming via Augmented Lagrangians: An Introduction with Computer Programs, Addison-Wesley Publishing Company, Reading, Massachusetts, 1975.

Bertsekas, D. P.,Multiplier Methods: a Survey, Automatica, Vol. 12, pp. 133?145, 1976.

Hestenes, M. R.,Optimization Theory: The Finite-Dimensional Case, John Wiley and Sons, New York, New York, 1975.

Mangasarian, O. L.,Unconstrained Lagrangians in Nonlinear Programming, University of Wisconsin, Computer Science Department, Technical Report No. 174, 1973.

Bertsekas, D. P.,On Penalty and Multiplier Methods for Constrained Minimization, Nonlinear Programming 2, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, New York, New York, 1975.

Fletcher, R.,A Class of Methods for Nonlinear Programming with Termination and Convergence Properties, Integer and Nonlinear Programming, Edited by J. Abadie, North-Holland Publishing Company, Amsterdam, Holland, 1970.

Mukai, H., andPolak, E.,A Quadratically Convergent Primal-Dual Algorithm with Global Convergence Properties for Solving Optimization Problems with Equality Constraints, Mathematical Programming, Vol. 9, pp. 336?349, 1975.

Fletcher, R.,An Exact Penalty Function for Nonlinear Programming with Inequalities, Mathematical Programming, Vol. 5, pp. 129?150, 1973.

Bertsekas, D. P.,Necessary and Sufficient Conditions for a Penalty Method to Be Exact, Vol. 9, pp. 87?99, 1975.

Tapia, R. A.,Quasi-Newton Methods for Equality Constrained Optimization: Equivalence of Existing Methods and a New Implementation, Nonlinear Programming 3, Edited by O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Academic Press, New York, New York, 1978.

Dixon, L. C. W.,Exact Penalty Function Methods in Nonlinear Programming, The Hatfield Polytechnic, Numerical Optimization Centre, Technical Report No. 103, 1979.

Bartholomew-Biggs, M. C.,The Recursive Quadratic Programming Approach to Constrained Optimization, Paper Presented at the 2nd IFAC Workshop on Control Applications of Nonlinear Programming and Optimization, Oberpfaffenhofen, Germany, 1980.

Di Pillo, G., andGrippo, L.,A New Class of Augmented Lagrangians in Nonlinear Programming, SIAM Journal on Control and Optimization, Vol. 17, pp. 618?628, 1979.

Di Pillo, G., Grippo, L., andLampariello, F.,A Method for Solving Equality Constrained Optimization Problems by Unconstrained Minimization, 9th IFIP Conference on Optimization Techniques, Edited by K. Iracki, K. Malanowski, and S. Walukiewicz, Springer-Verlag, Berlin, Germany, 1980.

Bertsekas, D. P.,Enlarging the Region of Convergence of Newton's Method for Constrained Optimization, Massachusetts Institute of Technology, Laboratory for Information and Decision Systems, Report No. 985, 1980.

Di Pillo, G., Grippo, L., andLampariello, F.,A Class of Methods for the Solution of Optimization Problems with Inequalities, Paper presented at the 10th IFIP Conference on System Modeling and Optimization, New York, 1981.