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In this paper, a derivative-free affine scaling linear programming algorithm based on probabilistic models is considered for solving linear inequality constrainted optimization problems. The proposed algorithm is designed to build probabilistic linear polynomial interpolation models using only n + 1 interpolation points for the objective function and reduce the computation cost for building interpolation function. We build the affine scaling linear programming methods which use probabilistic or random models and affine matrix within a classical linear programming framework. The backtracking line search technique can guarantee monotone descent of the objective function, and by using this technique, the new iterative points are located within the feasible region. Under some reasonable conditions, the global and local fast convergence of the algorithm is shown, and the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

A Derivative-Free Affine Scaling LP Algorithm Based on Probabilistic Models for Linear Inequality Constrained Optimization