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Results tagged with linear-programming
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user 53500
Questions on linear programming, the optimization of a linear function subject to linear constraints.
2
votes
1
answer
10k
views
Converting linear programming problems into standard form
I have the following linear programming problem:
Convert the following problems to standard form:
$$\begin{align}
\text{a)}&\text{minimize}&x+2y+3z\\
& \text{subject to}&2\le x+y\le 3\\
& …
- 8,669
4
votes
2
answers
805
views
Help with formulating a linear programming problem
I have the following linear programming problem I would like to be verified:
I have sketched the problem in the following picture:
Here is my attempted solution:
I figured that I have ten vari …
- 8,669
3
votes
1
answer
1k
views
Formulating a linear programming problem
I have the following problem:
Now I would like someone to verify whether my answer is correct or not :) Here goes:
If I denote the different alloys by $x_1, x_2, x_3, x_4, x_5$ I get
$$\text{mini …
- 8,669
0
votes
2
answers
3k
views
Help with proof: Hyperplane is an $(n-1)$-dimensional linear variety
I'm reading linear programming and I bumped into the following:
I'm having trouble getting grasp on the proof of proposition 2. Could someone perhaps explain it to me in other terms? For some reaso …
- 8,669
1
vote
1
answer
61
views
Why $(1,\textbf{0}) \not\in \{(r,\textbf{w}): r=tz_0-\textbf{c}^T\textbf{x}, \textbf{w}=t\te...
I'm learning about linear and nonlinear programming and on the chapter about duality I have the following statement and proof I can't understand:
minimize $\textbf{c}^T\textbf{x}$
subject to …
- 8,669
1
vote
1
answer
1k
views
Constructing canonical tableau for a linear programming problem involving SVM
I have the following set of inequalities and equalites
$$\begin{align}y_1x_1+\cdots +y_nx_n &= 0\\ x_1 &\geq
0\\\vdots\\x_n&\geq0 \\ x_1&\leq c\\\vdots \\x_n&\leq c,\end{align}$$
where $y_i\in …
- 8,669
0
votes
1
answer
49
views
Help with a property of a convex function
I'm studying linear and nonlinear programming and on my book I bumped into the following statement:
$$\lim_{\alpha \to 0} \displaystyle \frac{f(\textbf{x}+\alpha (\textbf{y}-\textbf{x}))-f(\textbf{x} …
- 8,669
2
votes
1
answer
398
views
Does the Duality Theorem of Linear Programming hold only in closed convex cones
I've just read the the Duality Theorem of Linear Programming. Here is the proof from my book (and my questions after it):
Duality Theorem of Linear Programming: If the primal or dual linear progr …
- 8,669
5
votes
1
answer
6k
views
Taylor's theorem for vector valued functions
I'm reading about linear and nonlinear programming and on one page I have the following statment (I have highlighted the areas where I have problems and drawn questions for them in the bottom of it):
…
- 8,669
2
votes
1
answer
524
views
First-order necessary condition for relative minimum point
I'm studying linear and nonlinear programming and I came across with the following proposition :
given $\rm x\in\Omega$ we are motivated to say that a vector $\mathbf d$ is a feasible direction at …
- 8,669
2
votes
0
answers
58
views
Calculating second derivative of $g(\alpha) = f(\textbf{y}(\alpha))$
I'm having problems with the second derivative of the function $g(\alpha) = f(\textbf{y}(\alpha))$ (which I will define more precisely below). I tried calculating it myself, could anyone just simply c …
- 8,669