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<p>In this paper we study a one-parameter regularization technique for Bolza problems of convex type with state constraints. Our regularization technique consists of applying Goebel’s self-dual regularization to the primal Lagrangian (which eliminates the state constraints) and whose main feature is that it simultaneously produces a dual Bolza problem having the same characteristics. The primal-dual approximations satisfy standard assumptions, and in particular, ensure the existence of absolutely continuous minimizing arcs. We establish that, under suitable conditions, any sequence of minimizers of the approximated primal problems admits a subsequence that converges, in the appropriate sense, to a minimizer of the original primal problem.</p>

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Self-dual Approximations to Convex Bolza Problems

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Cristopher Hermosilla,
  • Ernesto Treumún,
  • Peter Wolenski

摘要

In this paper we study a one-parameter regularization technique for Bolza problems of convex type with state constraints. Our regularization technique consists of applying Goebel’s self-dual regularization to the primal Lagrangian (which eliminates the state constraints) and whose main feature is that it simultaneously produces a dual Bolza problem having the same characteristics. The primal-dual approximations satisfy standard assumptions, and in particular, ensure the existence of absolutely continuous minimizing arcs. We establish that, under suitable conditions, any sequence of minimizers of the approximated primal problems admits a subsequence that converges, in the appropriate sense, to a minimizer of the original primal problem.