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nonsymmetric cone and Euclidean Jordan Algebra
Help me organize these concepts — KKT conditions and dual problemTangent Cone is a cone?Describing a Dual ConePropertise of a Dual ConeDifference between tangent cone and this constraint coneLinearizing coneConvex cone necessary and sufficient conditionWhat's the difference between linear space and cone?tangent cone and simplexThe Exponential Cone and Semi-definite programming
$begingroup$
I have a mathematical constraint which is a summation of exponential functions: $f = e^x + y$. Function $f$ is obviously convex. However, when I include this constraint in my model, MOSEK complains that the constraints with equations $f$ is a non symmetric cone. Upon doing a bit of research, I found notes about Euclidean Jordan Algebra being a unifying algebra for symmetric cones. I have 2 questions, (1) How do I prove that indeed the constraint with functions $f$ belongs in a non symmetric cone? (2) I do not understand how convexity relates to symmetric cones only as required by Euclidian Jordan Algebra. Please help?
convex-optimization
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
|
show 4 more comments
$begingroup$
I have a mathematical constraint which is a summation of exponential functions: $f = e^x + y$. Function $f$ is obviously convex. However, when I include this constraint in my model, MOSEK complains that the constraints with equations $f$ is a non symmetric cone. Upon doing a bit of research, I found notes about Euclidean Jordan Algebra being a unifying algebra for symmetric cones. I have 2 questions, (1) How do I prove that indeed the constraint with functions $f$ belongs in a non symmetric cone? (2) I do not understand how convexity relates to symmetric cones only as required by Euclidian Jordan Algebra. Please help?
convex-optimization
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53
|
show 4 more comments
$begingroup$
I have a mathematical constraint which is a summation of exponential functions: $f = e^x + y$. Function $f$ is obviously convex. However, when I include this constraint in my model, MOSEK complains that the constraints with equations $f$ is a non symmetric cone. Upon doing a bit of research, I found notes about Euclidean Jordan Algebra being a unifying algebra for symmetric cones. I have 2 questions, (1) How do I prove that indeed the constraint with functions $f$ belongs in a non symmetric cone? (2) I do not understand how convexity relates to symmetric cones only as required by Euclidian Jordan Algebra. Please help?
convex-optimization
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have a mathematical constraint which is a summation of exponential functions: $f = e^x + y$. Function $f$ is obviously convex. However, when I include this constraint in my model, MOSEK complains that the constraints with equations $f$ is a non symmetric cone. Upon doing a bit of research, I found notes about Euclidean Jordan Algebra being a unifying algebra for symmetric cones. I have 2 questions, (1) How do I prove that indeed the constraint with functions $f$ belongs in a non symmetric cone? (2) I do not understand how convexity relates to symmetric cones only as required by Euclidian Jordan Algebra. Please help?
convex-optimization
convex-optimization
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
asked Mar 12 at 8:50
P. KhozaP. Khoza
1
1
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
P. Khoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53
|
show 4 more comments
$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53
$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53
|
show 4 more comments
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$begingroup$
How exactly did you include that constraint in MOSEK and what was the error message? MOSEK version 9 supports the exponential cone even though it is not symmetric. These cones are also convex, and whether a solver supports them or not is a matter of choice. There are simply more efficient algorithms for symmetric cones than nonsymmetric ones.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:07
$begingroup$
Hi Michael,This is the actual constraint: $sumlimits_isumlimits_je^ln2(x_i + x_j) leq 0$
$endgroup$
– P. Khoza
Mar 12 at 9:31
$begingroup$
That doesn't explain how you inputted it in MOSEK and what error you exactly got. I am trying to find out if maybe it is some simple programming problem rather than a deep Jordan Algebra issue that you need help with.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:36
$begingroup$
I am using cvxpy and this is the snippet of the constraint:$(cp.exp(math.log(2) * (x[0] + x[0])) + (cp.exp(math.log(2) * (x[0] + x[1])) + (cp.exp(math.log(2) * (x[0] + x[2])) + (cp.exp(math.log(2) * (x[0] + x[3])) + (cp.exp(math.log(2) * (x[1] + x[0])) + (cp.exp(math.log(2) * (x[1] + x[1])) + vdots (cp.exp(math.log(2) * (x[3] + x[3])) <= 0$. The error message from Mosek is that this specific constraint is in the non symmetric cone.
$endgroup$
– P. Khoza
Mar 12 at 9:49
$begingroup$
You need cvxpy 1.0 AND Mosek 9 to solve a problem with exponential function. You get Mosek 9 from mosek.com/content/version-9-beta Is this what you have? You could also use the ECOS solver.
$endgroup$
– Michal Adamaszek
Mar 12 at 9:53