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<p>This paper addresses binary stochastic difference-of-convex (DC) programming problems with applications to stochastic shortest path routing. We propose two complementary approaches: a Sample Average Approximation (SAA)—based method that reformulates the problem into a large-sum DC program with binary variables, solved via DCA and stochastic DCA (SDCA) combined with an exact penalty technique; and a stochastic approximation (SA)—based approach that directly tackles the original stochastic DC problem through iterative stochastic DCA with penalized DC constraints. Numerical experiments on benchmark stochastic shortest path problems demonstrate the effectiveness and scalability of the proposed algorithms. The results highlight the efficiency and versatility of DCA for solving discrete stochastic DC programs, especially in large-scale settings.</p>

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Binary stochastic difference-of-convex optimization: DCA-based algorithms and application to a logistics routing problem

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Hoai An Le Thi,
  • Thi My Le Le

摘要

This paper addresses binary stochastic difference-of-convex (DC) programming problems with applications to stochastic shortest path routing. We propose two complementary approaches: a Sample Average Approximation (SAA)—based method that reformulates the problem into a large-sum DC program with binary variables, solved via DCA and stochastic DCA (SDCA) combined with an exact penalty technique; and a stochastic approximation (SA)—based approach that directly tackles the original stochastic DC problem through iterative stochastic DCA with penalized DC constraints. Numerical experiments on benchmark stochastic shortest path problems demonstrate the effectiveness and scalability of the proposed algorithms. The results highlight the efficiency and versatility of DCA for solving discrete stochastic DC programs, especially in large-scale settings.