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In this chapter, we present approaches for handling convex optimization problems featuring convex constraints. In particular, the latter are not assumed to be “known” analytically. That is, one can devise computational procedure to evaluate these constraints and obtain first-order information, but the constraints are not readily incorporated immediately within an optimization problem. We present various extensions of bundle methods to this setting as well as the supporting hyperplane method and a stabilized variant thereof.

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Methods for Non-linearly Constrained Non-smooth Optimization Problems

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  • 发表日期：

    2025年

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  • Wim Stefanus van Ackooij,
  • Welington Luis de Oliveira

摘要

In this chapter, we present approaches for handling convex optimization problems featuring convex constraints. In particular, the latter are not assumed to be “known” analytically. That is, one can devise computational procedure to evaluate these constraints and obtain first-order information, but the constraints are not readily incorporated immediately within an optimization problem. We present various extensions of bundle methods to this setting as well as the supporting hyperplane method and a stabilized variant thereof.