TOLMIN (optimization software)

TOLMIN ^[1][2] is a numerical optimization algorithm by Michael J. D. Powell. It is also the name of Powell's Fortran 77 implementation of the algorithm.

TOLMIN seeks the minimum of a differentiable nonlinear function subject to linear constraints (equality and/or inequality) and simple bounds on variables. Each search direction is calculated so that it does not intersect the boundary of any inequality constraint that is satisfied and that has a "small" residual at the beginning of the line search. The meaning of "small" depends on a parameter called TOL which is automatically adjusted, and which gives the name of the software.

Features of the software include: quadratic approximations of the objective function whose second derivative matrices are updated by means of the BFGS formula, active sets technique, primal-dual quadratic programming procedure for calculation of the search direction.

The TOLMIN software is distributed under The GNU Lesser General Public License (LGPL)^[2].

See also

• COBYLA
• UOBYQA
• NEWUOA
• BOBYQA
• LINCOA

References

External links

• A collection of optimization software written by Professor M. J. D. Powell at CCPForge
• A repository of Professor M. J. D. Powell's software
• Nonlinear Programming Packages --- TOLMIN

Optimization: Algorithms, methods, and heuristics   Unconstrained nonlinear: Methods calling … … functions Golden section search Interpolation methods Line search Nelder–Mead method Successive parabolic interpolation … and gradients Convergence Trust region Wolfe conditions Quasi–Newton BFGS and L-BFGS DFP Symmetric rank-one (SR1) Other methods Gauss–Newton Gradient Levenberg–Marquardt Conjugate gradient … and Hessians Newton's method   Constrained nonlinear General Barrier methods Penalty methods Differentiable Augmented Lagrangian methods Sequential quadratic programming Successive linear programming   Convex optimization Convex minimization Cutting-plane method Reduced gradient (Frank–Wolfe) Subgradient method Linear and quadratic Interior point Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-Exchange Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke   Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch & bound or cut Graph algorithms Minimum spanning tree Bellman–Ford Borůvka Dijkstra Floyd–Warshall Johnson Kruskal Network flows Dinic Edmonds–Karp Ford–Fulkerson Push-relabel maximum flow   Metaheuristics Evolutionary algorithm Hill climbing Local search Simulated annealing Tabu search Categories Algorithms and methods Heuristics Software