期刊
MATHEMATICAL PROGRAMMING
卷 144, 期 1-2, 页码 93-106出版社
SPRINGER
DOI: 10.1007/s10107-012-0617-9
关键词
Evaluation complexity; Worst-case analysis; Constrained nonlinear optimization
类别
资金
- EPSRC [EP/I028854/1, EP/E053351/1]
- Royal Society [14265]
- EPSRC [EP/I013067/1, EP/I028854/1, EP/E053351/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/I028854/1, EP/I013067/1, EP/E053351/1] Funding Source: researchfish
The complexity of finding -approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply.
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