Algorithms for Solving Non-Linear Programming Problems

Abstract

We consider the following problems

$$[tex]\min F(x),{X_1} = \left\{ {x \in {E_n};g(x) = 0,h(x) \le 0,0 \le x} \right\}[/tex]$$

((1))

$$[tex]\min F(x),{X_2} = \left\{ {x \in {E_n};g(x) = 0,h(x) \le 0} \right\}[/tex]$$

((2))

where F, g, h are continuously differentiate functions defined on E _n , Euclidean n space, x=[x ¹, x ²,..., x ⁿ] is a point in E _n , functions F, g, h define the mapping F: E _n →E ₁, define two open sets

$$[tex]X_1^0 = \left\{ {x:g(x) = 0,h(x) < 0,x > 0} \right\},X_2^0 = \left\{ {x:g(x) = 0,h(x) < 0} \right\}[/tex]$$