- 1 ABADIE, J., AND CARPENTIER, j. Generahzation of the Wolfe reduced gradient method to the case of nonlinear constraints In Optim,zatw~, R Fletcher, Ed., Academic Press, New York, 1969, pp 37-47Google Scholar
- 2 ABADIE, J. Application of the GRG algorithm to optimal control problems. In Nonlinear a~d Integer Programm~g, J Abadm, Ed, North-Holland Pub Co., Amsterdam, 1972, pp. 191-211.Google Scholar
- 3 BANDLER, J.W. internal reports m simulatmn, optimization and control. Faculty of Eng., VIcMaster U., Hamilton, Ont., Canada, Sept. 1976.Google Scholar
- 4 COHEN, C. Generalized reduced gradmnt technique for non-linear programming user wr~teup. Vogelback Comptng Ctr., Northeastern U., Boston, Mass., Feb. 1974.Google Scholar
- 5 COLVILLE, A R. A comparative study of nonlinear programming codes. Rep. 320-2949, IBM New York Sclentffic Center, 1968.Google Scholar
- 6 D.~.VIDON, W.C. Optimally conditioned optimization algorithms without line searches Math Programming 9, 1 (Aug. 1975), 1-30.Google Scholar
- 7 FLETCHER, R A new approach to variable metric algorithms Comptr. J. 13 (1970), 317-322.Google Scholar
- 8 FLETCHER, R. An ideal penalty function for constrained optimization. J. Inst. Math. Applicatw~s 15 (1975), 319-342.Google Scholar
- 9 GABAY, D., AND LUENBERGER, D. Efficiently convergmg minimization methods based on the reduced gradient. Internal Rep., Dept. of Eng.-Econ. Syst., Stanford U., Stanford, Calif , 1973.Google Scholar
- 10 GAGNON, C.G., ET .tL. A nonlinear programming approach to a very LARGE hydroelectric systems optimization. Math Programmzng 6 (1974), 28-41.Google Scholar
- 11 GLOVER, F., KARNEY, D., AND KLINGMAN, D. A comparison of computation times for various starting procedures, Basis change criteria, and solution algorithms for transportation problems. Management Sci. 20, 5 (1974), 793-814.Google Scholar
- 12 GOEFFRION, A., AND GRAVES, G Multicommodity distribution system design by Benders decomposition. Management 8c~. 20, 5 (1974), 822-844.Google Scholar
- 13 GOLDFARB, D. Extension of I)avidon's variable metric method to maximization under linear inequality and equality constraints. SIAM g. Appl. Math 17, 4 (July 1969), 739-764.Google Scholar
- 14 Harwell Subroutine Library Descriptions. Comptr. Sci. and Syst. })iv, Atomic Energy Res. Establishment, Harwell, Oxfordshire, England.Google Scholar
- 15 HELTNE, D.R., AND LITTSCHWAGER, J.M. Users guide for GRG 73 and technical appendices to GRG 73. College of Eng., U. of Iowa, Iowa City, Iowa, Sept. 1973.Google Scholar
- 16 HIMMELBL.~U, D M. Applied Nonlinear Programming. McGraw-Hill, New York, 1972.Google Scholar
- 17 LASDON, L S, Fox, R., .~ND RATNER, M. Nonlinear optimization using the generahzed reduced gradient method. Tech. Memo. 325, Dept of Oper. Res., Case Western Reserve U., Cleveland, Ohio, Oct 1973.Google Scholar
- 18 LASI)ON, L.S., WAREN, A.D., J.~IN, A., AND R.~.TNER, M. Design and testing of a GRG code for nonlinear optimization. Tech. Memo 20.353, Oper. Res. Dept, Case Western Reserve U., Cleveland, Ohio, March 1975.Google Scholar
- 19 L.~SDON, L S., Fox, R., RX~NER, M.W. An efficient one-dimensional search procedure for barrier functions. Math. Procramraing 4 (1973), 275-296.Google Scholar
- 20 MCCORMXCK, G.P. A mini-manual for use of the SUMT computer program and the factorable programming language. Tech. Rep. SOL-74-15, Dept of Oper Res., Syst. Optimization Lab., Stanford, Calif., 1974.Google Scholar
- 21 NEWELL, J S., AND HIMMELBLXU, D.M. A new method for nonlinearly constrained optimization. AICHE J. 21, 3 (May 1975), 479-486.Google Scholar
- 22 POWELL, M.J.D. A new algorithm for unconstrained optimization. In Nonlinear Programming, O L. Mangasarian and K Ritter, Eds., Academic Press, New York, 1970.Google Scholar
- 23 ROSEN, J.B., .~ND WAGNER, S. The GPM nonlinear programming subroutine package. Description and user instructions. Tech Rep. 75-9, Dept. of Comptr. and Inform. Sci., U. of Minnesota, Minneapolis, Minn , May 1975Google Scholar
- 24 SASSOON, A., .~ND MERRILL, H Some applications of optimization techniques to power systems problems. Proc. IEEE 62, 7 (July 1974), 959-975.Google Scholar
- 25 SHANNO, D F., AND PHU.~, K H. Inexact step lengths and quasi Newton methods. Working Paper, U of Toronto, Toronto, Ont., 1974.Google Scholar
- 26 SH.~NNO, D F., BERG, A., AND CHESTON, G. Restarts and rotatmns of quasi-Newton methods. In Informatwn Processing 74, North-Holland Pub. Co , Amsterdam, 1974, pp. 557-561.Google Scholar
Index Terms
- Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming
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