SNOPT Optional parameters - Revision history

Bjorn: /* Description of the optional parameters */

2013-08-14T15:17:38Z

Description of the optional parameters

← Older revision		Revision as of 10:17, 14 August 2013
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	\|0\|\|No minor iteration output except error messages.		\|0\|\|No minor iteration output except error messages.
	\|-		\|-
	\|''>= ''1\|\|A single line of output each minor iteration (controlled by Print frequency and Summary frequency).		\|''>='' 1\|\|A single line of output each minor iteration (controlled by Print frequency and Summary frequency).
	\|-		\|-
	\|''>= ''10\|\|Basis factorization statistics generated during the periodic refactorization of the basis (see Factorization frequency). Statistics for the ''first factorization ''each major iteration are controlled by the Major print level.		\|''>='' 10\|\|Basis factorization statistics generated during the periodic refactorization of the basis (see Factorization frequency). Statistics for the ''first factorization ''each major iteration are controlled by the Major print level.
	\|}		\|}

Bjorn: /* Description of the optional parameters */

2013-08-14T15:16:00Z

Description of the optional parameters

← Older revision		Revision as of 10:16, 14 August 2013
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	The density tolerance ''r''<sub>1</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 ''r''1 , the Markowitz strategy for choosing pivots is terminated. The remaining matrix is factored by a dense LU procedure. Raising the density tolerance towards 1.0 may give slightly sparser LU factors, with a slight increase in factorization time.		The density tolerance ''r''<sub>1</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 ''r''1 , the Markowitz strategy for choosing pivots is terminated. The remaining matrix is factored by a dense LU procedure. Raising the density tolerance towards 1.0 may give slightly sparser LU factors, with a slight increase in factorization time.

	The singularity tolerance ''r''<sub>2</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 r_2</math> or <math>\|U_{jj}\| < r_2 \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 ''r''<sub>2</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 r_2</math> or <math>\|U_{jj}\| < r_2 \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 a larger tolerance ''r''<sub>2</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 a larger tolerance ''r''<sub>2</sub> = 1.0e-5, say, may help cause a judicious change of basis.
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	\|}		\|}

	''i ''= 1 or 2 specifies minimization of <math>\|\|{x-x_0}\|\|_1</math> or <math>\frac{1}{2}\|\|{x-x_0}\|\|_2^2</math> when the starting point ''x''<sub>0</sub> is changed to satisfy the linear constraints (where ''x''0 refers to nonlinear variables).		''i ''= 1 or 2 specifies minimization of <math>\|\|{x-x_0}\|\|_1\,</math> or <math>\frac{1}{2}\|\|{x-x_0}\|\|_2^2</math> when the starting point ''x''<sub>0</sub> is changed to satisfy the linear constraints (where ''x''0 refers to nonlinear variables).

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Elias at 15:12, 9 December 2011

2011-12-09T15:12:47Z

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	If <math>\max_{j} \rho_j</math> is less than ''r ''times its previous value, another scaling pass is performed to adjust the row and column scales. Raising ''r ''from 0.9 to 0.99 (say) usually increases the number of scaling passes through ''A''. At most 10 passes are made.		If <math>\max_{j} \rho_j</math> is less than ''r ''times its previous value, another scaling pass is performed to adjust the row and column scales. Raising ''r ''from 0.9 to 0.99 (say) usually increases the number of scaling passes through ''A''. At most 10 passes are made.

	Scale Print causes the row-scales ''r''(''i'') and column-scales ''c''(''j'') to be printed. The scaled matrix coefficients are <math>\~~abar_~~{ij} = a_{ij} c(j) / r(i)</math>, and the scaled bounds on the variables and slacks are <math>\~~lbar_j~~ = l_j / c(j),\ ~~\ubar_j~~ = u_j / c(j)</math>		Scale Print causes the row-scales ''r''(''i'') and column-scales ''c''(''j'') to be printed. The scaled matrix coefficients are <math>\bar{a}_{ij} = a_{ij} c(j) / r(i)</math>, and the scaled bounds on the variables and slacks are <math>\bar{l}_j = l_j / c(j), \bar{u}_j = u_j / c(j)</math>

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Elias at 15:06, 9 December 2011

2011-12-09T15:06:17Z

← Older revision		Revision as of 10:06, 9 December 2011
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	<math>		<math>
	\left(\begin{array}{rrrrrr}{4 & -1 \\		\left(\begin{array}{rrrrrr}
			4 & -1 \\
	-1 & 4 & -1 \\		-1 & 4 & -1 \\
	& -1 & 4 & -1 \\		& -1 & 4 & -1 \\
	& & \ddots& \ddots& \ddots\\		& & \ddots& \ddots& \ddots\\
	& & & -1 & 4 & -1 \\		& & & -1 & 4 & -1 \\
	& & & & -1 & 4}		& & & & -1 & 4
	\end{array}\right),		\end{array}\right),
	</math>		</math>
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	</math>		</math>

	where <math>\v{viol}_i</math> is the violation of the ''i''th nonlinear constraint (''i ''= 1 : nnCon).		where <math>v{viol}_i</math> is the violation of the ''i''th nonlinear constraint (''i ''= 1 : nnCon).

	In the major iteration log, rowerr appears as the quantity labeled "Feasibl". If some of the problem functions are known to be of low accuracy, a larger Major feasibility tolerance may be appropriate.		In the major iteration log, rowerr appears as the quantity labeled "Feasibl". If some of the problem functions are known to be of low accuracy, a larger Major feasibility tolerance may be appropriate.
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	<math>		<math>
	\text{Comp}_j = ~~\left\{~~		\text{Comp}_j = \begin{array}{lcl}
	\begin{array}{lcl}		d_j \min{\{ x_j - l_j,1 \}} & & if d_j \ge 0\\
	\m d_j\min\{ x_j - l_j,1 \} & & ~~\hbox{~~if $d_j \ge 0~~$};~~		- d_j \min{\{ u_j - x_j,1 \}} & & if d_j < 0.
	\\~~[3pt]~~- d_j\min\{ u_j - x_j,1 \} & & ~~\hbox{~~if $d_j < 0$.}
	\end{array}		\end{array}
	~~\right.~~
	</math>		</math>

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	\|}		\|}

	''i ''= 1 or 2 specifies minimization of <math>~~\norm~~{x-x_0}_1</math> or <math>\~~half\norm~~{x-x_0}_2^2</math> when the starting point ''x''<sub>0</sub> is changed to satisfy the linear constraints (where ''x''0 refers to nonlinear variables).		''i ''= 1 or 2 specifies minimization of <math>\|\|{x-x_0}\|\|_1</math> or <math>\frac{1}{2}\|\|{x-x_0}\|\|_2^2</math> when the starting point ''x''<sub>0</sub> is changed to satisfy the linear constraints (where ''x''0 refers to nonlinear variables).

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	<math>		<math>
	v_i(~~x\kp1~~) \le \tau\max\{ 1, v_i(x_0) \},		v_i(x_{k+1}) \le \tau\max\{ 1, v_i(x_0) \},
	</math>		</math>

Elias: Created page with "{{Part Of Manual|title=the SNOPT Manual|link=SNOPT}} The performance of each SNOPT interface is controlled by a number of parameters or "options". Each option has a ..."

2011-10-13T13:04:17Z

Created page with "{{Part Of Manual|title=the SNOPT Manual|link=SNOPT}} The performance of each SNOPT interface is controlled by a number of parameters or "options". Each option has a ..."

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