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<p>Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.</p>

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Mixed-integer linearity in nonlinear optimization: a trust region approach

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月26日

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  • Alberto De Marchi

摘要

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential mixed-integer linearization with trust region safeguard, computing feasible iterates via calls to a generic mixed-integer linear solver. Convergence to critical, possibly suboptimal, feasible points is established for arbitrary starting points. Finally, we present numerical applications in nonsmooth optimal control and optimal network design and operation.