Optimization Linear Programming Quadratic Programming Unconstrained Optimization Constrained Optimization, Nonlinear Programming Linear Least Squares Constrained Nonlinear Least Squares Box-bounded Global Optimization Global Optimization, costly functions Mixed-Integer Programming Mixed-Integer Quadratic Programming Mixed-Integer Nonlinear Programming Semi-definite Programming

Box-bounded Global Optimization

 TOMLAB /SOL and TOMLAB /CGO TOMLAB /LGO

For box-bounded global optimization the TOMLAB Base Module solvers glbDirect and glcDirect are suitable. They utilize no derivative information and implement two slight variations of the DIRECT algorithm. For higher dimensions, the algorithm in glcDirect is often faster. The glcDirect implementation of DIRECT also handles linear and nonlinear constraints, and integer variables. Both solvers are implemented in C, and interfaced to MATLAB using mex file interfaces. The two solvers are also available as stand-alone products. Alternative FORTRAN implementations of glbDirect and glcDirect are callable as glbFast and glcFast, and slower MATLAB versions of the same algorithms are implemented in glbSolve and glcSolve. These DIRECT type of solvers have very good global search properties, but might need many function evaluations to obtain a high-accuracy solution. One way to achieve a better estimate of the global minimum is to run a local search, starting with the solution from the DIRECT solver. This will work if the problems are sufficiently smooth, enabling gradients to be estimated numerically by TOMLAB.

The hybrid solver glcCluster should be tested for all global optimization problem, preferably in combination with a fast local solver. glcCluster does a DIRECT search with e.g. glcDirect, then cluster all sampled points and runs a local search from the best point in each cluster. The likelihood is then very high that the global minimum is found with high accuracy.

The TOMLAB /CGO toolbox, aimed for costly (CPU-intensive, computionally expensive) black-box problems may also a good alternative, because the number of function evaluations needed to obtain the global minimum is normally very low. TOMLAB /LGO, the latest addition to the global optimization options in TOMLAB is an excellent option for all problems. See the LGO page for more information.

Solver reference:

 TOMLAB /CGO - rbfSolve TOMLAB /CGO - EGO TOMLAB /CGO - arbfMIP TOMLAB Base Module - glcCluster TOMLAB Base Module - glbDirect TOMLAB Base Module - glcDirect TOMLAB Base Module - glbSolve TOMLAB Base Module - glcSolve TOMLAB Base Module - glbFast TOMLAB Base Module - glcFast