NON-LINEAR PROGRAMMING PROBLEM

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Define general NLPP

Let z be a real value functions of n variables designed by,
(i)z=f(x1, x2 …xn)

(ii)Let b1, b2 …bn be a set of constraints
    s.t. g1(x1, x2. . . xn) (<=, =,or ,>=) b1
    s.t. g2(x1, x2. . . xn) (<=, =,or ,>=) b2
                                  .
                                  .
          gm(x1, x2. . . xn) (<=, =,or ,>=) bm
As in linear programming, f(x1, x2 …xn) is the NLP’s objective function, and            
 g1(x1, x2. . . xn) (<=, =,or ,>=) b1, . . . ,     gm(x1, x2. . . xn) (<=, =,or ,>=) bm
are the NLP’s constraints. An NLP with no constraints is an unconstrained NLP.

(iii)Let Xj>=0, j=1, 2…n
If either f or some g^i’s are non-linear. Then the problem of determining the type which makes z=0 is a maximum or minimum satisfies eqn (ii) & (iii). This is called general NLPP.

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