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<p>There recently has been much interest in studying optimization problems over circular cones due to their wide range of applications for the real-world problems. Since uncertainty often occurs in practical problems, in this paper we study a class of stochastic linear circular cone complementarity problems (SLCCCP). We present a deterministic formulation called expected value (EV) model for the SLCCCP. By using a smooth circular cone complementarity function, we reformulate the EV model as an unconstrained optimization problem and apply the sample average approximation (SAA) method to approximate it. Under suitable conditions, we prove that any accumulation point of optimal solutions (stationary points) of the SAA problem is an optimal solution (stationary point) of the original optimization problem with probability one. Moreover, we prove that the optimal value of the SAA problem has uniform exponential convergence. Finally, we give two numerical examples to show the effectiveness of the SAA method.</p>

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Expected value method for a class of stochastic linear circular cone complementarity problems

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Kaiyuan Guan,
  • Jingyong Tang

摘要

There recently has been much interest in studying optimization problems over circular cones due to their wide range of applications for the real-world problems. Since uncertainty often occurs in practical problems, in this paper we study a class of stochastic linear circular cone complementarity problems (SLCCCP). We present a deterministic formulation called expected value (EV) model for the SLCCCP. By using a smooth circular cone complementarity function, we reformulate the EV model as an unconstrained optimization problem and apply the sample average approximation (SAA) method to approximate it. Under suitable conditions, we prove that any accumulation point of optimal solutions (stationary points) of the SAA problem is an optimal solution (stationary point) of the original optimization problem with probability one. Moreover, we prove that the optimal value of the SAA problem has uniform exponential convergence. Finally, we give two numerical examples to show the effectiveness of the SAA method.