标题： 用于带线搜索的双层优化的顺序QCQP 显示英文标题

标题： Sequential QCQP for Bilevel Optimization with Line Search

摘要： 双层优化涉及一个层次结构，其中一个问题嵌套在另一个问题中，导致各层次之间复杂的相互依赖关系。 我们提出了一种单循环、无需调整参数的算法，该算法保证随时可行性，即近似满足下层最优条件，同时确保上层目标函数的下降。 在每次迭代中，一个具有显式解的凸二次约束二次规划（QCQP）产生搜索方向，随后采用受控制屏障函数启发的回溯线搜索，以确保安全且统一正的步长。 所提出的算法具有可扩展性，无需超参数调整，并在较弱的局部正规性假设下收敛。 我们建立了基于一阶平稳性度量的O(1/k)遍历收敛速率，并在典型的双层任务中验证了该算法的有效性。 显示英文摘要

摘要： Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility, i.e., approximate satisfaction of the lower-level optimality condition, while ensuring descent of the upper-level objective. At each iteration, a convex quadratically-constrained quadratic program (QCQP) with a closed-form solution yields the search direction, followed by a backtracking line search inspired by control barrier functions to ensure safe, uniformly positive step sizes. The resulting method is scalable, requires no hyperparameter tuning, and converges under mild local regularity assumptions. We establish an O(1/k) ergodic convergence rate in terms of a first-order stationary metric and demonstrate the algorithm's effectiveness on representative bilevel tasks.