Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization
Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization
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DOI：
10.1016/j.jco.2018.11.001
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发表时间：
2017-05
期刊：
影响因子：
--
通讯作者：
C. Cartis;N. Gould;P. Toint
中科院分区：
文献类型：
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作者：
C. Cartis;N. Gould;P. Toint
探讨了光滑非线性约束优化中高阶最优性的必要条件，并讨论了它们的内在复杂性。提出了一种近似一阶、二阶和三阶临界的两阶段最小化算法，并分析了其评估复杂度与求解两阶段子问题的内算法选择的函数关系。最后考虑了高阶临界和惩罚技术之间的关系，表明标准算法方法在寻求近似约束高阶临界点时会失败。
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.