Applied nonlinear programming by Sanjay Sharma

By Sanjay Sharma

Sharma S. utilized Nonlinear Programming (New Age overseas (P) Ltd, 2006)(ISBN 812241771X)

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2 An open box of rectangular cross-section. Solution.

10) are used to solve the problem. A unique solution is obtained for wi, i = 1, 2,.... N if N = n + 1, as will be observed later. This type of problem is having zero degree of difficulty as N – n – 1 = 0, where degree of difficulty = (N – n – 1). A comparatively complicated problem may occur if N > (n + 1) because degree of difficulty > 1. ( f * )wN FM I FM I =G H w JK GH w JK * 1 w1 * 2 1 w2 ... 8), f* = M*i M* M* M* or f * = 1 = 2 = ... = N wi w1 w2 wN a a a As Mi* = ci . x1* 1i . x2* 2i ... x2* ni , * f = LM C Nw 1 1 .

E. 009. e. 3. 2 UNIVARIATE METHOD This is suitable for a multivariable problem. One variable is chosen at a time and from an initial point, it is increased or decreased depending on the appropriate direction in order to minimize the function. An optimum step length may be determined as illustrated in the example. Similarly each variable is changed, one at a time, and that is why the name “univariate method”. One cycle is said to complete when all the variables have been changed. The next cycle will start from this position.

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