Add-in for solvers of unconstrained minimization to eliminate lower bounds of variables by transformation. (English) Zbl 1458.90587
Summary: The paper considers the issue of implementation of a software add-in, which transforms minimization problems with constraints only on lower bounds of variables to unconstrained ones. The add-in eliminates lower bounds of variables through their transformation, without creation of new auxiliary variables. The add-in can be included in any algorithm of unconstrained minimization, which has certain design. At the same time, any number of suitable transformations of variables can be included into the add-in.
The add-in is implemented in C++ and consists of three components: small collection of transformations of variables; small collection of minimization test-problems with constraints only on lower bounds of variables; stopping conditions of minimization algorithms and program-driver.
In the numerical experiments, mainly CG-DESCENT-C-6.8 and l-bfgs were used. Results show that empowering unconstrained minimization algorithms by such add-in is a promising direction, especially, for symmetric matrix games. Materials of experiments are uploaded at GitHub: https://github.com/kobage.
The add-in is implemented in C++ and consists of three components: small collection of transformations of variables; small collection of minimization test-problems with constraints only on lower bounds of variables; stopping conditions of minimization algorithms and program-driver.
In the numerical experiments, mainly CG-DESCENT-C-6.8 and l-bfgs were used. Results show that empowering unconstrained minimization algorithms by such add-in is a promising direction, especially, for symmetric matrix games. Materials of experiments are uploaded at GitHub: https://github.com/kobage.
MSC:
| 90C30 | Nonlinear programming |
| 90-04 | Software, source code, etc. for problems pertaining to operations research and mathematical programming |
Keywords:
box-constrained optimization; elimination of lower bounds; unconstrained optimization; symmetric matrix game; l-bfgs; CG-DESCENT; modified heavy ball; MINOS; GUROBIReferences:
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