# myTOMLAB  
*TOMLAB Base Module
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Solves sparse or dense nonlinear least squares optimization problems with explicit handling of linear inequality and equality constraints and simple bounds on the variables. The solver is suitable for ill-conditioned nonlinear least squares problems and nonlinear systems of equations. It may also be used for linear least squares.

Seven methods are implemented:

Method Reference
Fletcher-Xu hybrid method (default)  Fletcher, Xu 1987
Al-Baali-Fletcher hybrid method Al-Baali, Fletcher 1986
Huschens TSSM method Huschens, SIAM J. Optimization. Vol 4, No 1, pp 108-129,1994
Gauss-Newton with subspace minimization
Wang, Li, Qi Structured MBFGS method
Li-Fukushima MBFGS method
Broydens method

  Main features:

  • An active-set strategy by Björkman and Holmström handles simple bounds and linear constraints
  • If rank problem occurs, the solver is using subspace minimization techniques. A rank tolerance parameter may be set by the user.
  • The equation systems are solved with sparse or dense QR-factorization, in both cases using pivoting. Using dense SVD (singular value decomposition) is an option.
  • If the flag Prob.LargeScale is set, clsSolve is using the sparse QR package sqr2. clsSolve then can avoid forming the m by m orthogonal Q matrix. Otherwise, if the number of residuals, m, is very large, this Q matrix occupies very much memory.
  • For illustrative purposes, the equation system may also be solved with the pseudoinverse (pinv) in Matlab or the built-in inverse. These methods are not for practical use.
  • The line search is a modified version of an algorithm by Fletcher (1987)
  • The hybrid methods are using BFGS safeguarded quasi-Newton updates. The initial matrix may be given by the user.
  • The initial feasible point is found solving a special quadratic programming problem. This problem is solved by QPOPT in Tomlab /MINOS or qpSolve in the Tomlab Base Module.
  • If missing, unknown gradients and Jacobians are estimated using any of the Tomlab methods.
  • Since no second order derivative information is used, clsSolve may not be able to determine the type of stationary point converged to.

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