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<p>In this paper, we have considered a class of optimization problems called as multi-objective semi-infinite optimization problem with vanishing constraints. For this class of optimization problem, stationary points and constraint qualification in terms of convexificators have been introduced and Karush-Kuhn-Tucker (KKT) necessary and sufficient optimality conditions have been derived. We have used pseudo and quasi convexity assumptions to derive sufficient conditions. Moreover, an application of our problem in structural optimization has been presented. The model to find an optimized truss structure with minimum weight has been developed for the first time based on semi-infinite and vanishing constraints. One such type of example is also considered and solved using MATLAB. Further, the obtained solution is also verified using the theorems developed in this paper. Non-trivial examples have also been formulated and placed at suitable places to verify the results obtained in this paper properly.</p>

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Semi-infinite vanishing constraints problem with convexificators and optimality analysis

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Mahamadsohil A. Arora,
  • Indira P. Tripathi

摘要

In this paper, we have considered a class of optimization problems called as multi-objective semi-infinite optimization problem with vanishing constraints. For this class of optimization problem, stationary points and constraint qualification in terms of convexificators have been introduced and Karush-Kuhn-Tucker (KKT) necessary and sufficient optimality conditions have been derived. We have used pseudo and quasi convexity assumptions to derive sufficient conditions. Moreover, an application of our problem in structural optimization has been presented. The model to find an optimized truss structure with minimum weight has been developed for the first time based on semi-infinite and vanishing constraints. One such type of example is also considered and solved using MATLAB. Further, the obtained solution is also verified using the theorems developed in this paper. Non-trivial examples have also been formulated and placed at suitable places to verify the results obtained in this paper properly.