MINOS Solver Options - Revision history

Bjorn: /* Options for All Problems */

2013-08-14T13:36:18Z

Options for All Problems

← Older revision		Revision as of 09:36, 14 August 2013
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	This causes various amounts of information to be output to the Print file. Most debug levels are not helpful to normal users, but they are listed here for completeness.		This causes various amounts of information to be output to the Print file. Most debug levels are not helpful to normal users, but they are listed here for completeness.

	{\| class="wikitable"		{\|class="wikitable"
	\|-valign="top"		\|-valign="top"
	\|''l ''= 0\|\|No debug output.		\|''l'' = 0 \|\| No debug output.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 2\|\|(or more) Output from m5setx showing the maximum residual after a row check.		\|''l'' = 2\|\|(or more) Output from m5setx showing the maximum residual after a row check.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 40\|\|Output from lu8rpc (which updates the ''LU ''factors of the basis matrix), showing the position of the last nonzero in the transformed incoming column.		\|''l'' = 40\|\|Output from lu8rpc (which updates the ''LU ''factors of the basis matrix), showing the position of the last nonzero in the transformed incoming column.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 50\|\|Output from lu1mar (which computes the ''LU ''factors each refactorization), showing each pivot row and column and the dimensions of the dense matrix involved in the associated elimination.		\|''l'' = 50\|\|Output from lu1mar (which computes the ''LU ''factors each refactorization), showing each pivot row and column and the dimensions of the dense matrix involved in the associated elimination.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 100\|\|Output from m2bfac and m5log listing the basic and superbasic variables and their values at every iteration.		\|''l'' = 100\|\|Output from m2bfac and m5log listing the basic and superbasic variables and their values at every iteration.
	\|}		\|}

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	{\| cellpadding="10"		{\| cellpadding="10"
	\|<tt>Pivot tolerance</tt>\|\|<tt>t</tt>\|\|<tt>Default = E<sup>2/3</sup> ≈ 10<sup>-11</sup>		\|<tt>Pivot tolerance</tt>\|\|<tt>t</tt>\|\|<tt>Default = E<sup>2/3</sup> ≈ 10<sup>-11</sup></tt>
	\|}		\|}

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	{\| class="wikitable"		{\| class="wikitable"
	\|-valign="top"		\|-valign="top"
	\|''l ''= 0\|\|No scaling. If storage is at a premium, this option saves ''m ''+ ''n ''words of workspace.		\|''l'' = 0\|\|No scaling. If storage is at a premium, this option saves ''m ''+ ''n ''words of workspace.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 1\|\| Linear constraints and variables are scaled by an iterative procedure that attempts to make the matrix coefficients as close as \|possible to 1.0. This sometimes improves the performance of the solution procedures.		\|''l'' = 1\|\| Linear constraints and variables are scaled by an iterative procedure that attempts to make the matrix coefficients as close as \|possible to 1.0. This sometimes improves the performance of the solution procedures.
	\|-valign="top"		\|-valign="top"
	\|''l ''= 2\|\|All constraints and variables are scaled by the iterative procedure. Also, a certain additional scaling is performed that may be \|helpful if the right-hand side ''b ''or the solution ''x ''is large. This takes into account columns of ( ''A I '') that are fixed or have positive lower bounds or negative upper bounds.		\|''l'' = 2\|\|All constraints and variables are scaled by the iterative procedure. Also, a certain additional scaling is performed that may be \|helpful if the right-hand side ''b ''or the solution ''x ''is large. This takes into account columns of ( ''A I '') that are fixed or have positive lower bounds or negative upper bounds.
	\|}		\|}

Bjorn: /* Options for All Problems */

2013-08-14T12:51:23Z

Options for All Problems

← Older revision		Revision as of 08:51, 14 August 2013
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	The density tolerance ''t''<sub>3</sub> is used during ''LU ''factorization of the basis matrix. Columns of ''L ''and rows of ''U ''are formed one at a time, and the remaining rows and columns of the basis are altered appropriately. At any stage, if the density of the remaining matrix exceeds ''t''<sub>3</sub>, the Markowitz strategy for choosing pivots is altered to reduce the time spent searching for each remaining pivot. Raising the density tolerance towards 1.0 may give slightly sparser ''LU ''factors, with a slight increase in factorization time.		The density tolerance ''t''<sub>3</sub> is used during ''LU ''factorization of the basis matrix. Columns of ''L ''and rows of ''U ''are formed one at a time, and the remaining rows and columns of the basis are altered appropriately. At any stage, if the density of the remaining matrix exceeds ''t''<sub>3</sub>, the Markowitz strategy for choosing pivots is altered to reduce the time spent searching for each remaining pivot. Raising the density tolerance towards 1.0 may give slightly sparser ''LU ''factors, with a slight increase in factorization time.

	The singularity tolerance ''t''<sub>4</sub> helps guard against ill-conditioned basis matrices. When the basis is refactorized, the diagonal elements of ''U ''are tested as follows: if <math>\|U_{jj}\| \le t_4</math> or <math>\|U_{jj}\| < t_4 \max_i \|U_{ij}\|</math>, the ''j''-th column of the basis is replaced by the corresponding slack variable. (This is most likely to occur after a restart, or at the start of a major iteration.)		The singularity tolerance ''t''<sub>4</sub> helps guard against ill-conditioned basis matrices. When the basis is refactorized, the diagonal elements of ''U ''are tested as follows: if <math>\|U_{jj}\| \le t_4</math> or <math>\|U_{jj}\| < t_4 \times \max_i \|U_{ij}\|</math>, the ''j''-th column of the basis is replaced by the corresponding slack variable. (This is most likely to occur after a restart, or at the start of a major iteration.)

	In some cases, the Jacobian matrix may converge to values that make the basis exactly singular. (For example, a whole row of the Jacobian could be zero at an optimal solution.) Before exact singularity occurs, the basis could become very ill-conditioned and the optimization could progress very slowly (if at all). Setting ''t''<sub>4</sub> = 1.0e-5, say, may help cause a judicious change of basis.		In some cases, the Jacobian matrix may converge to values that make the basis exactly singular. (For example, a whole row of the Jacobian could be zero at an optimal solution.) Before exact singularity occurs, the basis could become very ill-conditioned and the optimization could progress very slowly (if at all). Setting ''t''<sub>4</sub> = 1.0e-5, say, may help cause a judicious change of basis.
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	{\| cellpadding="10"		{\| cellpadding="10"
	\|<tt>		\|<tt>Optimality tolerance</tt>\|\|<tt>t</tt>\|\|<tt>Default = 1.0e-6</tt>
	Optimality tolerance</tt>\|\|<tt>t</tt>\|\|<tt>Default = 1.0e-6</tt>
	\|}		\|}

Elias at 13:57, 9 December 2011

2011-12-09T13:57:34Z

← Older revision		Revision as of 09:57, 9 December 2011
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	Broadly speaking, the pivot tolerance is used to prevent columns entering the basis if they would cause the basis to become almost singular. When ''x ''changes to ''x ''+ ''αp ''for some search direction ''p'', a "ratio test" is used to determine which component of ''x ''reaches an upper or lower bound first. The corresponding element of ''p ''is called the pivot element.		Broadly speaking, the pivot tolerance is used to prevent columns entering the basis if they would cause the basis to become almost singular. When ''x ''changes to ''x ''+ ''αp ''for some search direction ''p'', a "ratio test" is used to determine which component of ''x ''reaches an upper or lower bound first. The corresponding element of ''p ''is called the pivot element.

	For linear problems, elements of ''p ''are ignored (and therefore cannot be pivot elements) if they are smaller than the pivot tolerance ''t''. For nonlinear problems, elements smaller than <math>t~~\norm~~{p}</math> are ignored.		For linear problems, elements of ''p ''are ignored (and therefore cannot be pivot elements) if they are smaller than the pivot tolerance ''t''. For nonlinear problems, elements smaller than <math>t\|\|{p}\|\|</math> are ignored.

	It is common for two or more variables to reach a bound at essentially the same time. In such cases, the Feasibility tolerance provides some freedom to maximize the pivot element and thereby improve numerical stability. Excessively small Feasibility tolerances should therefore not be specified.		It is common for two or more variables to reach a bound at essentially the same time. In such cases, the Feasibility tolerance provides some freedom to maximize the pivot element and thereby improve numerical stability. Excessively small Feasibility tolerances should therefore not be specified.

Elias at 13:51, 9 December 2011

2011-12-09T13:51:23Z

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Elias: Created page with "The following sections describes some of the solver options depending on problem type. ==Options for Linear Programming== The following options apply specifically to linear pro..."

2011-09-06T09:33:24Z

Created page with "The following sections describes some of the solver options depending on problem type. ==Options for Linear Programming== The following options apply specifically to linear pro..."

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