MISQP - Revision history

Bjorn: /* Overview */

2014-10-09T13:54:31Z

Overview

← Older revision		Revision as of 08:54, 9 October 2014
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	Welcome to the TOMLAB /MISQP User's Guide. TOMLAB /MISQP includes the MISQP and MIQL solvers from Klaus Schittkowski and an interface to The MathWorks' MATLAB.		Welcome to the TOMLAB /MISQP User's Guide. TOMLAB /MISQP includes the MISQP and MIQL solvers from Klaus Schittkowski and an interface to The MathWorks' MATLAB.

	~~TOMLAB /~~MISQP solves mixed-integer nonlinear mathematical programming problems with equality and inequality constraints. It is assumed that integer variables have a ''smooth'' influence on the model functions, i.e., that function values do not change drastically when in- or decrementing an integer value.		MISQP solves mixed-integer nonlinear mathematical programming problems with equality and inequality constraints. It is assumed that integer variables have a ''smooth'' influence on the model functions, i.e., that function values do not change drastically when in- or decrementing an integer value.

	The internal algorithm uses a modified sequential quadratic approximation method, stabilized by a trust region method including Yuan's second order corrections. The Hessian of the Lagrangian function is approximated by BFGS updates subject to the continous and integer variables.		The internal algorithm uses a modified sequential quadratic approximation method, stabilized by a trust region method including Yuan's second order corrections. The Hessian of the Lagrangian function is approximated by BFGS updates subject to the continous and integer variables.

	~~TOMLAB /~~MIQL solves strictly convex mixed-integer quadratic mathematical programming problems with linear equality and inequality constraints. The mixed-integer problem is solved by a branch-and-cut algorithm.		MIQL solves strictly convex mixed-integer quadratic mathematical programming problems with linear equality and inequality constraints. The mixed-integer problem is solved by a branch-and-cut algorithm.

	===Contents of this Manual===		===Contents of this Manual===

Bjorn: /* Description of Inputs */

2013-08-19T14:41:47Z

Description of Inputs

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	1 - (default 1).		1 - (default 1).
	\|-~~valign="top"~~		\|-
	\|'''\|\|		\|''\|\|

	Options for the MIQP subsolver MIQL:		''Options for the MIQP subsolver MIQL:''

	\|-valign="top"		\|-valign="top"

Bjorn: /* qlTL */

2013-08-16T06:53:08Z

qlTL

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	===qlTL===		===qlTL===

			====Purpose====
	Solves strictly convex quadratic programming problems.		Solves strictly convex quadratic programming problems.

Bjorn: /* qlTL */

2013-08-14T12:19:14Z

qlTL

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	QL solves problems of the form		QL solves problems of the form

			<div class="center">
	<math>		<math>
	\begin{array}{ll}		\begin{array}{ll}
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	\end{array}		\end{array}
	</math>		</math>
			</div>

Bjorn: /* Purpose */

2013-08-14T12:18:27Z

Purpose

← Older revision		Revision as of 07:18, 14 August 2013
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	</math>		</math>
	</div>		</div>


	where <math>x,x_{L},x_{U}\in \mathbb{R}^{n}</math>, <math>A\in \mathbb{R}^{m_{1}\times n}</math> and <math>b_{L},b_{U}\in \mathbb{R}^{m_{1}}</math> and <math>c(x),c_{L},c_{U}\in \mathbb{R} ^{m_{2}}</math>, Furthermore, <math>x_i,\, i\in\mathbb{I}</math> are restricted to integer values only.		where <math>x,x_{L},x_{U}\in \mathbb{R}^{n}</math>, <math>A\in \mathbb{R}^{m_{1}\times n}</math> and <math>b_{L},b_{U}\in \mathbb{R}^{m_{1}}</math> and <math>c(x),c_{L},c_{U}\in \mathbb{R} ^{m_{2}}</math>, Furthermore, <math>x_i,\, i\in\mathbb{I}</math> are restricted to integer values only.

Bjorn: /* Purpose */

2013-08-14T12:18:18Z

Purpose

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	\begin{array}{cccccc}		\begin{array}{cccccc}
	\min\limits_{x} & f(x) \\		\min\limits_{x} & f(x) \\
			& \\
	s/t & x_{L} & \leq & x & \leq & x_{U} \\		s/t & x_{L} & \leq & x & \leq & x_{U} \\
	& b_{L} & \leq & Ax & \leq & b_{U} \\		& b_{L} & \leq & Ax & \leq & b_{U} \\

Bjorn: /* Purpose */

2013-08-14T12:17:33Z

Purpose

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	\begin{array}{ll}		\begin{array}{ll}
	\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x\\		\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x\\
			& \\
	s/t & \begin{array}{lcccl}		s/t & \begin{array}{lcccl}
	x_{L} & \leq & x & \leq & x_{U} \\		x_{L} & \leq & x & \leq & x_{U} \\

Bjorn: /* Purpose */

2013-08-14T12:15:55Z

Purpose

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	where <math>c, x \in \mathbb{R}^n</math>, <math>F \in \mathbb{R}^{n \times n}</math> and positive definite, <math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in \mathbb{R}^{n+m_1}</math>.		where <math>c, x, x_L, x_U \in \mathbb{R}^n</math>, <math>F \in \mathbb{R}^{n \times n}</math> and positive definite, <math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in \mathbb{R}^{m_1}</math>.

	The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.		The variables <math>x \in I</math>, the index subset of <math>1,...,n</math>, are restricted to be integers.

Bjorn: /* qlTL */

2013-08-14T12:14:03Z

qlTL

← Older revision		Revision as of 07:14, 14 August 2013
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	QL solves problems of the form		QL solves problems of the form


	<math>		<math>
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	& \\		& \\
	s/t & \begin{array}{lcccl}		s/t & \begin{array}{lcccl}
	& & x & &, \\		x_{L} & \leq & x & \leq & x_{U} \\
	b_{L} & \leq & A x & \leq & b_{U} \\		b_{L} & \leq & A x & \leq & b_{U} \\
	\end{array}		\end{array}
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	</math>		</math>

	where <math>c, x \in \mathbb{R}^n</math>, <math>F \in \mathbb{R}^{n \times n}</math> and positive definite,
	<math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in \mathbb{R}^{n+m_1}</math>.		where <math>c, x, x_L, x_U \in \mathbb{R}^n</math>, <math>F \in \mathbb{R}^{n \times n}</math> and positive definite,
			<math>A \in \mathbb{R}^{m_1 \times n}</math>, and <math>b_L,b_U \in \mathbb{R}^{m_1}</math>.

	====Calling Syntax====		====Calling Syntax====

Bjorn: /* Purpose */

2013-08-14T12:09:26Z

Purpose

← Older revision		Revision as of 07:09, 14 August 2013
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	\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x\\		\min\limits_{x} & f(x) = \frac{1}{2} x^T F x + c^T x\\
	s/t & \begin{array}{lcccl}		s/t & \begin{array}{lcccl}
	& & x & &, \\		x_{L} & \leq & x & \leq & x_{U} \\
	b_{L} & \leq & A x & \leq & b_{U} \\		b_{L} & \leq & A x & \leq & b_{U} \\
	\end{array}		\end{array}