A notation to represent that all elements of a vector must be less than zero?
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I am defining an optimization algorithm. One of the constraints of the length $p$ vector $boldsymbol{theta}^-$ is that all elements in that vector must be less than or equal to zero.
I could say that
$$ theta^+_j leq 0quad forall jin{1 ... p}.$$
Is there any way to express this in the form
$$boldsymbol{theta}^+ leq 0?$$
That doesn't make a lot of sense, but is there some alternate symbol or notation I could replace for $leq$ to express that I want the vector to be element-wise less than or equal to zero?
inequality notation vectors
asked Nov 15 at 16:31
kingledion
1284
add a comment |
up vote
1
down vote
favorite
I am defining an optimization algorithm. One of the constraints of the length $p$ vector $boldsymbol{theta}^-$ is that all elements in that vector must be less than or equal to zero.
I could say that
$$ theta^+_j leq 0quad forall jin{1 ... p}.$$
Is there any way to express this in the form
$$boldsymbol{theta}^+ leq 0?$$
That doesn't make a lot of sense, but is there some alternate symbol or notation I could replace for $leq$ to express that I want the vector to be element-wise less than or equal to zero?
inequality notation vectors
asked Nov 15 at 16:31
kingledion
1284
2
Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
1
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am defining an optimization algorithm. One of the constraints of the length $p$ vector $boldsymbol{theta}^-$ is that all elements in that vector must be less than or equal to zero.
I could say that
$$ theta^+_j leq 0quad forall jin{1 ... p}.$$
Is there any way to express this in the form
$$boldsymbol{theta}^+ leq 0?$$
That doesn't make a lot of sense, but is there some alternate symbol or notation I could replace for $leq$ to express that I want the vector to be element-wise less than or equal to zero?
inequality notation vectors
asked Nov 15 at 16:31
kingledion
1284
I am defining an optimization algorithm. One of the constraints of the length $p$ vector $boldsymbol{theta}^-$ is that all elements in that vector must be less than or equal to zero.
I could say that
$$ theta^+_j leq 0quad forall jin{1 ... p}.$$
Is there any way to express this in the form
$$boldsymbol{theta}^+ leq 0?$$
That doesn't make a lot of sense, but is there some alternate symbol or notation I could replace for $leq$ to express that I want the vector to be element-wise less than or equal to zero?
inequality notation vectors
inequality notation vectors
asked Nov 15 at 16:31
kingledion
1284
asked Nov 15 at 16:31
kingledion
1284
asked Nov 15 at 16:31
kingledion
1284
asked Nov 15 at 16:31
kingledion
1284
asked Nov 15 at 16:31
kingledion
1284
1284
2
Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
1
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39
add a comment |
2
Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
1
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39
2
2
Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
1
1
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39
add a comment |
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Why not just use words? You, and your readers, presumably share a language, so write in that language. If you really must, and intend to use this notation a lot of times, you could just define a symbol to mean what you say ($preccurlyeq$ is unlikely to clash with anything else), but in most cases the notation that you want is the string of symbols "has all elements less than or equal to zero" or similar.
– user3482749
Nov 15 at 16:37
1
I agree, if you were struggling to find a suitable notation for it with symbols yourself as the writer, who is to say that your reader would understand the symbols you decided to use? Don't discount the usefulness of using words rather than symbols to express an idea.
– JMoravitz
Nov 15 at 16:39