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Computational Ecology and Software, 2026, 16(4): 273-286
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Article

Projective scaling method for single objective linear optimization problems based on projection operations

Muhammad Tlas
Scientific Services Department, Atomic Energy Commission, P. O. Box 6091, Damascus, Syria

Received 7 May 2026;Accepted 13 May 2026;Published online 23 May 2026;Published 1 December 2026
IAEES

Abstract
An interior point algorithm to solve single objective linear programming problems has been proposed in this paper. The method uses the projection operation of the gradient of the objective function onto the null space of the feasible region in order to generate, at each iterate, an interior search direction. It can be taken an interior step from the current iterate to the next one along this feasible direction. During the execution of the algorithm, a sequence of interior points will be generated. It has been proved that this sequence converges to an ε-optimal solution, where ε is a predetermined error tolerance known a priori. Numerical single objective linear optimization problems of different kinds, feasible, infeasible and unbounded are illustrated using this algorithm.

Keywords linear programming;linear optimization;projection operation;Interior point method;scaling algorithm.


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