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This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. [ABSTRACT FROM AUTHOR]