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 Jan 25 comment Why does an argument similiar to 0.999…=1 show 999…=-1? Dec 18 comment Using dot product when finding shortest distance between a line and a point, not working The dot product is an operation you can do on two vectors. If you are careful to distinguish between Vectors and Points, you could mechanically tell that Q \dot P doesn't have meaning. Oct 14 awarded Necromancer 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).