An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents

Algorithm 1

Original algorithm.

(1)	Step 0 (initialization). Set , . By using formulas (22) and (23), the ratio used for the two consecutive segments in each dimension is , which subdivides into smaller rectangles. Represent the vertex of each small rectangle as , which is stored in the set .
(2)	Step 1. Select a point from the , solve the linear programming problem , and let .
(3)	Step 2. If the problem is solvable, then , and let ; if , let , , ; if , set and go to Step 1; otherwise, the algorithm terminates; let