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A Deep-Cutting-Plane Technique for Reverse Convex Optimization.

K Moshirvaziri, M A Amouzegar

    IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
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    Summary
    This summary is machine-generated.

    This study introduces deep-cutting-plane techniques for reverse-convex programs, enhancing optimization efficiency. The novel method improves bounds iteratively, leading to faster convergence in complex problem-solving.

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    Area of Science:

    • Optimization Theory
    • Applied Mathematics
    • Computational Science

    Background:

    • Cutting-plane methods are effective for convex and combinatorial optimization.
    • Their application to non-convex optimization shows promise.
    • Deep cuts are crucial for efficiently reducing search domains.

    Purpose of the Study:

    • Develop deep-cutting-plane techniques for reverse-convex programs.
    • Improve the efficiency of global solution search in optimization.
    • Provide a robust algorithm for complex optimization problems.

    Main Methods:

    • Utilizing deep-cutting-plane techniques.
    • Iteratively updating and improving upper and lower bounds for optimal values.
    • Employing fathoming strategies for search domain subdivisions.

    Main Results:

    • Demonstrated effectiveness of deep cuts in reverse-convex programming.
    • Algorithm successfully finds, updates, and improves bounds.
    • Termination achieved when bounds converge or subdivisions are fathomed.

    Conclusions:

    • Deep-cutting-plane techniques offer a promising approach for reverse-convex optimization.
    • The developed algorithm provides computational efficiency.
    • Numerical results and an illustrative example validate the method's efficacy.