Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models

@article{Birgin2016EvaluationCF,
title={Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models},
author={Ernesto G. Birgin and J. L. Gardenghi and Jos{\'e} Mario Mart{\'i}nez and Sandra A. Santos and Philippe L. Toint},
journal={SIAM Journal on Optimization},
year={2016},
volume={26},
pages={951-967}
}
The evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's functions and their first $p$ derivatives. This is achieved by using a two-phase algorithm inspired by Cartis, Gould, and Toint [SIAM J. Optim., 21 (2011), pp. 1721--1739; SIAM J. Optim… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 18 CITATIONS

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• ArXiv
• 2018
VIEW 14 EXCERPTS
CITES BACKGROUND, METHODS & RESULTS
HIGHLY INFLUENCED

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• 2018
VIEW 13 EXCERPTS
CITES BACKGROUND, RESULTS & METHODS
HIGHLY INFLUENCED

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• ArXiv
• 2017
VIEW 7 EXCERPTS
CITES BACKGROUND, METHODS & RESULTS
HIGHLY INFLUENCED

Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization

• J. Complexity
• 2017
VIEW 8 EXCERPTS
CITES BACKGROUND, METHODS & RESULTS
HIGHLY INFLUENCED

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VIEW 8 EXCERPTS
CITES METHODS, BACKGROUND & RESULTS
HIGHLY INFLUENCED

An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem

VIEW 12 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

VIEW 2 EXCERPTS
CITES BACKGROUND

Direct search based on probabilistic feasible descent for bound and linearly constrained problems

• Comp. Opt. and Appl.
• 2019
VIEW 1 EXCERPT
CITES METHODS

• ArXiv
• 2019
VIEW 2 EXCERPTS
CITES BACKGROUND

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

VIEW 2 EXCERPTS
CITES BACKGROUND

References

Publications referenced by this paper.
SHOWING 1-10 OF 22 REFERENCES

Sur les ensembles semi-analytiques

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

On the Evaluation Complexity of Cubic Regularization Methods for Potentially Rank-Deficient Nonlinear Least-Squares Problems and Its Relevance to Constrained Nonlinear Optimization

• SIAM Journal on Optimization
• 2013
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

Mart́ınez. On sequential optimality conditions for smooth constrained optimization

R. Andreani, G. Haeser, J.M
• Optimization, 60:627–641,
• 2011
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences

• SIAM Journal on Optimization
• 2010
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods

• SIAM Journal on Optimization
• 1999
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Corrigendum: On the complexity of finding first-order critical points in constrained nonlinear optimization

• Math. Program.
• 2017
VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

On the Evaluation Complexity of Composite Function Minimization with Applications to Nonconvex Nonlinear Programming

• SIAM Journal on Optimization
• 2011
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

• Math. Program.
• 2017
VIEW 3 EXCERPTS

On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization

• Math. Program.
• 2015
VIEW 1 EXCERPT

VIEW 1 EXCERPT