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<p>We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums of functions. Unlike the classical Haar duality scheme, these dual problems provide zero duality gap and are solvable under the standard Slater condition. We derive general optimality conditions/multiplier rules by applying subdifferential rules for infinite sums established in Hantoute, A J. Optim. Theory Appl. 2026, <a href="https://doi.org/10.1007/s10957-025-02916-w">https://doi.org/10.1007/s10957-025-02916-w</a>,</p>

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Strong Duality in Infinite Convex Optimization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月6日

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  • Abderrahim Hantoute,
  • Alexander Y. Kruger,
  • Marco A. López

摘要

We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums of functions. Unlike the classical Haar duality scheme, these dual problems provide zero duality gap and are solvable under the standard Slater condition. We derive general optimality conditions/multiplier rules by applying subdifferential rules for infinite sums established in Hantoute, A J. Optim. Theory Appl. 2026, https://doi.org/10.1007/s10957-025-02916-w,