Representations of quasi-Newton matrices and their use in limited memory methods
Mathematical Programming: Series A and B
Line search algorithms with guaranteed sufficient decrease
ACM Transactions on Mathematical Software (TOMS)
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
An SQP method for general nonlinear programs using only equality constrained subproblems
Mathematical Programming: Series A and B
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Exclusion Regions for Systems of Equations
SIAM Journal on Numerical Analysis
Mathematical Programming: Series A and B
Line Search Filter Methods for Nonlinear Programming: Local Convergence
SIAM Journal on Optimization
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence
SIAM Journal on Optimization
On the Convergence of Successive Linear-Quadratic Programming Algorithms
SIAM Journal on Optimization
Mathematical Programming: Series A and B
An interior algorithm for nonlinear optimization that combines line search and trust region steps
Mathematical Programming: Series A and B
The design of the Boost interval arithmetic library
Theoretical Computer Science - Real numbers and computers
FILIB++, a fast interval library supporting containment computations
ACM Transactions on Mathematical Software (TOMS)
Adaptive Barrier Update Strategies for Nonlinear Interior Methods
SIAM Journal on Optimization
Convexity and Concavity Detection in Computational Graphs: Tree Walks for Convexity Assessment
INFORMS Journal on Computing
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We compare six state-of-the-art local optimization solvers, with a focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check indicator (measuring whether the local minimizers found are good candidates for near-optimal verified feasible points), a function value indicator (measuring the contribution to the progress of the global search), and a running time indicator (estimating the computational cost of the local search within the global search). The solvers are compared on the COCONUT Environment test set consisting of 1307 problems. Our main goal is to predict the behavior of the solvers in terms of the three performance indicators on a new problem. For this we introduce a $k$-nearest neighbor method applied over a feature space consisting of several categorical and numerical features of the optimization problems. The quality and robustness of the prediction is demonstrated by various quality measurements with detailed comparative tests. In particular, we found that on the test set we are able to pick a “best” solver in 66-89% of the cases and avoid picking all “useless” solvers in 95-99% of the cases (when a useful alternative exists). The resulting automated solver selection method is implemented as an inference engine of the COCONUT Environment.