User talk:Wotao.yin - Revision history

Dattorro at 02:23, 6 November 2010

2010-11-06T02:23:30Z

←Older revision		Revision as of 02:23, 6 November 2010
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	Nonnegative rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes directly from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.		Nonnegative rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes directly from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.

-	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.	+	Notation <math>\mbox{vec}\,X\!\in\mathbb{R}^{262144}</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.

	Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.		Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.
-	~~It contains only~~ integers from the set <math>\{{-1},0,1,2\}\,</math>.	+	All its entries are integers from the set <math>\{{-1},0,1,2\}\,</math>.
	The 2 appears only in the fifth row from the bottom of <math>A\,</math>.		The 2 appears only in the fifth row from the bottom of <math>A\,</math>.

Dattorro at 02:19, 6 November 2010

2010-11-06T02:19:48Z

←Older revision		Revision as of 02:19, 6 November 2010
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	</center>		</center>

-	~~Rectangular~~ submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.	+	Nonnegative rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes directly from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.

	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.		Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.

Dattorro at 02:19, 6 November 2010

2010-11-06T02:19:07Z

←Older revision		Revision as of 02:19, 6 November 2010
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	Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value.		Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value.

-	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before numerical solution begins.   The [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] possesses all 262,144 columns of <math>A\,</math>;   none of its columns have been discarded in a presolve.	+	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before numerical solution begins.   The [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] possesses all 262,144 columns of <math>A\,</math>;   none of its columns have yet been discarded by a presolve.

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

Dattorro at 02:17, 6 November 2010

2010-11-06T02:17:32Z

←Older revision		Revision as of 02:17, 6 November 2010
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	Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.		Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.

-	A Matlab binary ~~containing~~ matrices <math>\,A</math> and <math>\,b</math> is	+	A [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] contains matrices <math>\,A</math> and <math>\,b</math>.
-	~~[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here]~~.	+	Vector <math>c\,</math> is left unspecified because I want to vary it later as part of a
-	Vector <math>c\,</math> is left unspecified because I want to vary it later as part of a ~~convex iteration~~.	+	[[Convex Iteration]].
	Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value.		Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value.

Dattorro at 02:14, 6 November 2010

2010-11-06T02:14:50Z

Dattorro at 11:28, 5 November 2010

2010-11-05T11:28:13Z

←Older revision		Revision as of 11:28, 5 November 2010
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	For your purposes, <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.		For your purposes, <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.

-	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.   The Matlab binary above ~~has~~ all columns of <math>A\,</math>;   none of its columns have been discarded.	+	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before numerical solution begins.   The Matlab binary above possesses all columns of <math>A\,</math>;   none of its columns have been discarded.


	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

Dattorro at 11:21, 5 November 2010

2010-11-05T11:21:13Z

Dattorro at 11:07, 5 November 2010

2010-11-05T11:07:07Z

←Older revision		Revision as of 11:07, 5 November 2010
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	&X\geq_{}\mathbf{0}\end{array}</math>		&X\geq_{}\mathbf{0}\end{array}</math>
	</center>		</center>
-
-	Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.
-	For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.

	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.		Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.
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	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.		A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.
		+
		+	A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is
		+	[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here].
		+	Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.
		+	For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

Dattorro at 10:57, 5 November 2010

2010-11-05T10:57:30Z

←Older revision		Revision as of 10:57, 5 November 2010
Line 11:		Line 11:
	For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.		For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.

-	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a ~~square~~ permutation matrix <math>\,\Xi\!\in\mathbb{R}^{1024\times1024}\,</math> having three out of every ~~consecutive~~ four columns discarded.	+	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.
		+
		+	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.

	Matrix <math>A\in\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.		Matrix <math>A\in\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.
-	It contains integers from the set <math>\{-1,0,1,2\}</math>.	+	It contains integers from the set <math>\{{-1},0,1,2\}\,</math>.

-	Vector <math>b\,</math> is quite sparse having only a single nonzero entry.	+	Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.

-	A good presolver can eliminate about 60,000 columns of <math>A\,</math> because one of the constraints (fifth row from the bottom) has ~~all~~ nonnegative entries. This means that about 60,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.	+	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

Dattorro at 10:43, 5 November 2010

2010-11-05T10:43:57Z

←Older revision		Revision as of 10:43, 5 November 2010
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-	~~Wotao~~	+	I regard the following as a difficult problem, having spent considerable time with it.
-		+
-	I regard the following as a difficult problem, having spent considerable time on it.	+

	<center>		<center>
Line 11:		Line 9:

	Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.		Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.
-	~~To start~~, it may be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.	+	For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.
-	Rectangular ~~matrix~~ <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a square permutation matrix <math>\Xi\,</math> having three out of every consecutive four columns discarded.	+
		+	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a square permutation matrix <math>\,\Xi\!\in\mathbb{R}^{1024\times1024}\,</math> having three out of every consecutive four columns discarded.
		+
		+	Matrix <math>A\in\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.
		+	It contains integers from the set <math>\{-1,0,1,2\}</math>.
		+
		+	Vector <math>b\,</math> is quite sparse having only a single nonzero entry.
		+
		+	A good presolver can eliminate about 60,000 columns of <math>A\,</math> because one of the constraints (fifth row from the bottom) has all nonnegative entries. This means that about 60,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

←Older revision		Revision as of 02:14, 6 November 2010
Line 10:		Line 10:
	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.		Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.

-	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.	+	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.

	Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.		Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.
-	It ~~only~~ contains integers from the set <math>\{{-1},0,1,2\}\,</math>.	+	It contains only integers from the set <math>\{{-1},0,1,2\}\,</math>.
		+	The 2 appears only in the fifth row from the bottom of <math>A\,</math>.

	Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.		Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.
Line 19:		Line 20:
	A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is		A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is
	[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here].		[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here].
-	Vector <math>c\,</math> is left unspecified ~~beause~~ I ~~may~~ want to vary it later in a convex iteration.	+	Vector <math>c\,</math> is left unspecified because I want to vary it later as part of a convex iteration.
-	~~For your purposes,~~ <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.	+	Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value.
-		+
-	~~A good presolver can eliminate about 50~~,~~000 columns of <math>\~~,~~A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries~~ in permutation submatrix <math>X\,</math> can be set to zero before numerical solution begins.   The Matlab binary above possesses all columns of <math>A\,</math>;   none of its columns have been discarded.	+

		+	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before numerical solution begins.   The [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] possesses all 262,144 columns of <math>A\,</math>;   none of its columns have been discarded in a presolve.

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)

←Older revision		Revision as of 11:21, 5 November 2010
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-	I regard the following as a difficult problem, having spent considerable time with it.	+	I regard the following as a very difficult problem, having spent considerable time with it.

	<center>		<center>
Line 8:		Line 8:
	</center>		</center>

-	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.	+	Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded.   This discard occurs because of structural redundancy in <math>\Xi\,</math>.

	Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.		Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom.

-	Matrix <math>A\in\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.	+	Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros.
-	It contains integers from the set <math>\{{-1},0,1,2\}\,</math>.	+	It only contains integers from the set <math>\{{-1},0,1,2\}\,</math>.

	Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.		Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>.
-
-	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.

	A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is		A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is
-	[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here].	+	[http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here].
-	Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.	+	Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration.
-	For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.	+	For your purposes, <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>.
		+
		+	A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries.   This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins.   The Matlab binary above has all columns of <math>A\,</math>;   none of its columns have been discarded.
		+

	--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)		--[[User:Dattorro\|Dattorro]] 03:31, 5 November 2010 (PDT)