Programming non-linear

Grossmann, I. E., Mixed-Integer Non-Linear Programming Techniques for the Synthesis of Engineering Systems, Res. Eng. Design, 1 205, 1990. 

H. W. Kuhn and A. W. Tucker, Non-linear Programming, in J. Neyman, ed., Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, 1951 Thomas L. Saaty, Mathematical Methods of Operations Research, McGraw-Hill Book Co., New York, 1959. 

WILLIAMS, N. (1967) Linear and Non-linear Programming in Industry (Pitman). 

Jang, S. S., Josepth, B and Mukai, H. (1986). Comparison of two approaches to on-line parameter and state estimation problem of non-linear systems. Ind. Eng. Chem. Process Des. Dev. 25, 809-814. Jazwinski, A. H. (1970). Stochastic Processes and Filtering Theory. Academic Press, New York. Liebman, M. J., Edgar, T. F., and Lasdon, L. S. (1992). Efficient data reconciliation and estimation for dynamic process using non-linear programming techniques. Comput. Chem. Eng. 16, 963-986. McBrayer, K. F., and Edgar, T. F. (1995). Bias detection and estimation on dynamic data reconciliation. J Proc. Control 15, 285-289. 

Kim, I. W., Liebman, M. J., and Edgar, T. E (1990). Robust error-in-variable estimation using non-linear programming techniques. AIChE J. 36, 985-993. 

Liebman, M. J., Edgar, T. F., and Lasdon, L. S. (1992). Efficient data reconciliation and estimation for dynamic process using non-linear programming techniques. Comput. Chem. Eng. 16,963-986. 

Rosen, J. B. (1961). The gradient projection method for non-linear programming, Part II, Non-linear constraints. J. Soc. Indus. Appl. Math., 9, 414-32. 

Kunzi, H.P., Krelle, W. and W. Oettli, Non-Linear Programming, Blaisdell, Waltham, Massachusetts (1966). 

If the resulting simultaneous equations are linear, their solution is a straightforward matter, but it is easy to see that in our case the equations will not be linear, and thus the minimization of equation (5) subject to equation (9) is an example of a non-linear programming problem. 

Non-linear programming is a fast growing subject and much research is being done and many new algorithms appear every year. It seems to the Reporters that the current area of major interest in the field is the area of variable-metric methods, particularly those not needing accurate linear searches. Unfortunately, from a quantum chemical point of view, such methods are liable to be of use only in exponent and nuclear position optimization and in this context, as we have seen, Newton-like methods are also worth serious consideration. 

Wolfe, P. (1962) Notices Am Math Soc 9, 308. Methods of non-linear programming. 

A. K. Sunol, A Mixed Integer (Non) Linear Programming Approach to Simultaneous Design of Product and Process , in L. T. Biegler and M. F. Doherty (eds.). Fourth... 

A.V. Fiacco and G.P. McCormik, Non-Linear Programming Sequential Unconstrained Optimization Technique, Wiley, New York. 

To optimize a chromatographic assay, Weyland et al. reported the application of an operational research technique called non-linear programming. 

Caf Saccharin,benzoic acid Optimization separation by non-linear programming Lichrosorb RP8 lOum 250x4.6 ACN-Me0H-H 0 in various ratios 202 ... 

Mixed fnleger Non-Linear Program Solver SiiTkuiation equaCicre for individual piafits and Mnneclions. 

Owens and Wendt applied only two liquids to form drops in their experimental surface tension determinations. They used fw = 21.8 and y(v =51.0 for water, and y= 49.5 and y[v = 1.3 mj m 2 for methylene iodide, in their calculations. After measuring the contact angles of these liquid drops on polymers, they solved Equation (693) simultaneously for two unknowns of yfv and y( v, so that it would then be easy to calculate the total surface tension of the polymer from the (ysv = yfv + 7sv) equation. Later, Kaelble extended this approach and applied determinant calculations to determine ysv and y(v- When the amount of contact angle data exceeded the number of equations, a non-linear programming method was introduced by Erbil and Meric in 1988. 

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