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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F * = 215. 2. 1, a problem concerning fabrication of a cylindrical box is discussed with the objective of minimizing total relevant cost, which is the sum of transportation and fabrication cost. F. 4). This is as followsf (r, h) = 200 πr 2 + 460 πrh + 360 −2 −1 r h π Apply the geometric programming. Solution. F. 554 m f * = Rs. 3. An industry wants to fabricate an open box of mild steel as shown in Fig. 2. This box of rectangular cross-section will be used for transporting certain volume of small items for a project.

5 − m2 ) + + 4. 59 ( 0. 5) − 8. 88 = 0 ( 0. 5 − m ) 2 Value of m needs to be obtained which will satisfy above equation. 5. S. of equation obtained in terms of m are as follows: 11. S. 2. S. 37. e. 17). 44 + 0. 10 The procedure is continued for any number of cycles till improvement in function values are observed by varying x1 and x2 each. The exact optimum is [x1*, x2*] = [1/3, 1/9]. J GG . JJ GH x JK 1 2 n This is transformed to an unconstrained minimization problem by using penalty parameter and constraints in a suitable form.

Consider a function f(x1, x2). Optimum x1 and x2 are to be obtained in order to minimize f(x 1, x 2). Fig. 2 is a representation of the univariate method. x2 Initial point 1’ m (x1, x2) n 2’ 3’ 1 2 3 (x1*, x2*) x1 Fig. 2 Changing one variable at a time. From the initial point (x1, x2), only x1 is varied. In order to find out suitable direction, probe length is used. Probe length is a small step length by which the current value of any variable is increased or decreased, so that appropriate direction may be identified.

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