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A numerical optimization approach based on the sequential quadratic programming (SQP) algorithm is used to determine the optimum texture shape for generating the highest load-carrying capacity (LCC). A benchmark problem is first solved to validate this optimization method. Then the novel texture shapes which produce the maximum LCC for both unidirectional and bidirectional sliding motion are proposed and analyzed. For unidirectional sliding the optimum textures have chevron-type shapes with flat fronts and for bidirectional sliding they consist of pairs of the trapezoid-like shapes. Finally, the performances of optimum shapes are compared with those of regular shapes using a mass-conservative algorithm.