统一的漏斗恢复 SQP 算法
A Unified Funnel Restoration SQP Algorithm
AI总结：
提出统一双循环非线性优化框架及带可行性恢复的漏斗 SQP 算法，证明信赖域版本全局收敛，并在 Uno 与 CUTEst 上验证。
摘要：
我们考虑非线性约束优化问题，并讨论一种由四个算法组成部分构成的通用双循环框架，该框架统一了广泛的非线性优化求解器。此框架已在开源求解器 Uno 中实现；Uno 是一个类似瑞士军刀的 C++ 优化框架，统一了许多非线性约束非凸优化求解器。我们通过一种序列二次规划（SQP）算法来说明该框架，该算法对约束违反度维持一个可接受的上界，称为漏斗，并通过单调降低该漏斗来控制迭代点的可行性。不可行的二次子问题由可行性恢复策略处理。全局化由线搜索或信赖域方法控制。我们基于滤子法的已有结果，证明了信赖域漏斗 SQP 方法的全局收敛性。我们在 Uno 中实现了该算法，并给出了信赖域线搜索漏斗 SQP 在小型 CUTEst 实例上的大量测试结果。
英文摘要：
We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.
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