Reputation
355
Top tag
Next privilege 500 Rep.
Access review queues
Badges
2 15
Impact
~30k people reached

  • 0 posts edited
  • 0 helpful flags
  • 35 votes cast
Jul
25
awarded  Popular Question
Jun
3
revised Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities
added 237 characters in body
Jun
3
comment Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities
Let me state it a different way. If you give me $A,b$ corresponding to $Ax\geq b$, I can give you a $C,d$ such that a solution of $y$ in $Cy=d, y\geq 0$ corresponds to a solution of $x$ in your original problem. If you want to avoid the trivial solution, then solve $Ax \geq \epsilon\mathbf{1}$ where $\mathbf{1}$ is an appropriately sized vector of $1$s and $\epsilon$ is some very small number greater than zero.
Jun
3
comment Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities
I have already in my question repeated what you are asking for. Do you see that? I have not misread your question. These two equations are both forms of linear programming problem. You can convert from one form to another. Can you explain why you need the strict inequality in your application?
Jun
3
answered Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities
May
28
revised What exactly is the difference between a derivative and a total derivative?
rewordings, included two more ways to say the same thing.
May
23
comment What exactly is the difference between a derivative and a total derivative?
If $x$ is secretly a function of $t$, then the notation $\frac{\text{d}}{\text{d}t} f(x,t)$ is called the total derivative and is an abbreviation for the (single-variable derivative) $g'(t)$ where $g(t)=f(x(t),t)$. In applying the chain rule to the last expression, you would need some way to denote "the derivative of $f$ with respect to its first argument" many people would write $\frac{\partial}{\partial x} f$ for this, but in many cases this is confusing.
May
23
comment Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
@HagenvonEitzen what is the claim that you are referring to? I am saying that you could define the number we call sqrt(2) as the length of the diagonal of a unit square, right? My objection is to the claim that sqrt(2) is only defined algebraically as the root of something.
May
23
comment Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
The length of a diagonal of a unit square is sqrt(2). The length of a diagonal of a unit cube is sqrt(3). That's how people discovered irrational numbers, as far as I can tell. It wasn't algebra.
May
23
comment What exactly is the difference between a derivative and a total derivative?
@HenningMakholm, I clarified and reorganized. I hope the point is clearer now! Since you are CS/PL person, I think you can help me make this even clearer. What I'm really getting at is some distinction between a function and an expression and named arguments versus positional arguments. People get confused because of a scoping issue. in the expression ∂f(x,y)/∂x, the x in the denominator is named argument of f. The x in the numerator is something else: a variable defined in the current scope.
May
23
revised What exactly is the difference between a derivative and a total derivative?
reorganization, clarification
May
22
comment What exactly is the difference between a derivative and a total derivative?
In my original answer, I have "the total derivative usually means..." Do you think I need to make this stand out typographically?
May
22
comment What exactly is the difference between a derivative and a total derivative?
I think one conclusion from the wall-o-text is that the concept of "total derivative" is due to sloppiness in math notation, and that we are better off without it. As such, I don't think there IS a clear definition. Do you see what I mean?
May
20
revised What exactly is the difference between a derivative and a total derivative?
typos and clarifications
May
20
revised What exactly is the difference between a derivative and a total derivative?
added 20 characters in body
May
4
comment connection among big-M, Lagrangian, Pentalty Method, and Augmented Lagrangian
I don't understand your second comment mentioning the constraint $(x-1)^2 \leq 0$. Is that in reference to an example in my question or is that your own example? I can sort of understand why the Lagrange multipliers would be wonky. If you tighten the left-hand-side of that constraint, then there is no $x$ that satisfies is
May
4
comment connection among big-M, Lagrangian, Pentalty Method, and Augmented Lagrangian
@Michael thanks for the comments. feel free to make an answer. The reason I say "fighting does not happen with linear objectives" (with linear penalty) is because I'm thinking of the big-$M$ method as a sort of penalty method. It's not exactly, because the penalty term is not squared. But you do choose an $M$ large enough to drive a variable to be zero (it can't go negative because of the non-negativity constraint in the standard form of a linear program).
Apr
29
revised connection among big-M, Lagrangian, Pentalty Method, and Augmented Lagrangian
edited tags
Apr
27
awarded  Promoter
Apr
27
revised connection among big-M, Lagrangian, Pentalty Method, and Augmented Lagrangian
added 13 characters in body