<?xml version="1.0" encoding="UTF-8"?>
<osil xmlns="os.optimizationservices.org" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="os.optimizationservices.org C:\DataFiles\RESEARCH\OS\OS-trunk-work\OS\schemas\OSiL.xsd">
	<instanceHeader>
		<name>SDPA1</name>
		<source>
			created by H.I. Gassmann from the description of the SDPA format 
			found at htp://plato.asu.edu/ftp/sdpa_format.txt</source>
		<description>
			This is a very small semidefinite program:
			
			min 10x1 + 20x2
			st  X = F1x1 + F2x2 - F0
			    X positive semidefinite
			    
			where F0 = [ 1 0 0 0
			                     0 2 0 0
			                     0 0 3 0
			                     0 0 0 4]
			                     
			            F1 = [1 0 0 0
			                     0 1 0 0
			                     0 0 0 0
			                     0 0 0 0]
			                     
			            F2 = [0 0 0 0
			                     0 1 0 0 
			                     0 0 5 2
			                     0 0 2 6]
			                     
			This version tries to exploit the block structure of the matrices as stipulated in the SDPA format.
		</description>
	</instanceHeader>	
	<instanceData>
		<variables numberOfVariables="7">
			<var lb="-INF" ub="INF" mult="7"></var>
		</variables>
		<objectives>
			<obj maxOrMin="min" numberOfObjCoef="2">
				<coef idx="0">10.</coef>
				<coef idx="1">20.</coef>
			</obj>
		</objectives>
		<matrices numberOfMatrices="7">
			<constantMatrix numberOfColumns="2" id="F01" numberOfRows="2">
				<elements numberOfValues="2">
					<start>
						<el>0</el>
						<el>1</el>
						<el>2</el>
					</start>
					<rowIdx>
						<el>0</el>
						<el>1</el>
					</rowIdx>
					<value>
						<el>1.</el>
						<el>2.</el>
					</value>
				</elements>
			</constantMatrix>			
			<constantMatrix numberOfColumns="2" id="F02" numberOfRows="2">
				<elements numberOfValues="2">
					<start>
						<el>0</el>
						<el>1</el>
						<el>2</el>
					</start>
					<rowIdx>
						<el>0</el>
						<el>1</el>
					</rowIdx>
					<value>
						<el>3.</el>
						<el>4.</el>
					</value>
				</elements>
			</constantMatrix>			
			<constantMatrix numberOfColumns="2" id="F11" numberOfRows="2">
				<elements numberOfValues="2">
					<start>
						<el>0</el>
						<el>1</el>
						<el>2</el>
					</start>
					<rowIdx>
						<el>0</el>
						<el>1</el>
					</rowIdx>
					<value>
						<el>1.</el>
						<el>1.</el>
					</value>
				</elements>
			</constantMatrix>
			<constantMatrix numberOfColumns="2" id="F21" numberOfRows="2">
				<elements numberOfValues="1">
					<start>
						<el>0</el>
						<el>0</el>
						<el>1</el>
					</start>
					<rowIdx>
						<el>1</el>
					</rowIdx>
					<value>
						<el>1.</el>
					</value>
				</elements>
			</constantMatrix>
			<constantMatrix numberOfColumns="2" id="F22" numberOfRows="2">
				<elements numberOfValues="3"  symmetric="true">
					<start>
						<el>0</el>
						<el>1</el>
						<el>3</el>
					</start>
					<rowIdx>
						<el>0</el>
						<el>0</el>
						<el>1</el>
					</rowIdx>
					<value>
						<el>5.</el>
						<el>2.</el>
						<el>6.</el>
					</value>
				</elements>
			</constantMatrix>
			<linearMatrix numberOfColumns="2" id="X1" numberOfRows="2" symmetric="true" numberOfEl="2" numberOfBlocks="0">
				<el rowIdx="0" colIdx="0" varIdx="2"/>
				<el rowIdx="1" colIdx="1" varIdx="3"/>
			</linearMatrix>
			<linearMatrix numberOfColumns="2" id="X2" numberOfRows="2" symmetric="true" numberOfEl="0" numberOfBlocks="0" varIdxStart="4" varIdxEnd="6"/>
		</matrices>
		<cones numberOfCones="1">
			<semidefiniteCone numberOfColumns="2" id="C0" numberOfRows="2"/>
		</cones>
		<matrixProgramming>
			<matrixVariables numberOfMatrixVar="2">
				<matrixVar matrixID="X1" lbConeId="C0"/>
				<matrixVar matrixID="X2" lbConeId="C0"/>
			</matrixVariables>
			<matrixConstraints numberOfMatrixCon="2">
				<matrixCon numberOfRows="1" numberOfCols="1" lbMatrixID="F01" ubMatrixID="F01"/>			
				<matrixCon numberOfRows="1" numberOfCols="1" lbMatrixID="F02" ubMatrixID="F02"/>			
			</matrixConstraints>
			<linearConstraintMatrixOperators numberOfOperators="5">
				<matrixVarOperator matrixVarIdx="0" matrixConIdx="0" scalarCoef="-1"/>
				<scalarVarOperator varIdx="0" matrixConIdx="0" matrixID="F11"></scalarVarOperator>
				<scalarVarOperator varIdx="1" matrixConIdx="0" matrixID="F21"></scalarVarOperator>
				<matrixVarOperator matrixVarIdx="1" matrixConIdx="1" scalarCoef="-1"/>
				<scalarVarOperator varIdx="1" matrixConIdx="1" matrixID="F22"></scalarVarOperator>
			</linearConstraintMatrixOperators>
		</matrixProgramming>
		</instanceData>
</osil>
