0
votes
1answer
54 views

Relation between arg min of two functions

When is $u_F(x) = \underset{u}{\text{argmin}}(F_1(x),\cdots,F_u(x),\cdots,F_U(x))$ $\le$ $\underset{u}{\text{argmin}}(G_1(x),\cdots,G_u(x),\cdots,G_U(x)) = u_G(x)$ where $u \in \{1,2,\cdots,U\}, x \in ...
0
votes
0answers
59 views

Simply formulated but hard problem on system of linear equations

When does the below system has a solution? $$AX=B\\ X > 0$$, where $A$ is $n\times n$ symmetric positive definite matrix and $X$ is a $n\times 1 $ column vector. Note: (I'm trying to use Farka's ...
0
votes
1answer
123 views

How to answer this linear algebra question, which is related to operations research?

I have the following question: Let $A$ be an $(m \times n)$-matrix and $b$ a vector in $\mathbb{R}^m$. The system of inequalities $Ax \leq b$ has a solution $x \geq 0$, if and only if $yb \geq 0$ for ...
0
votes
1answer
166 views

Edge weight function for graph instance of scheduling and allocation problem

I have difficulties developing a proper (non-scalar) edge cost function $c_e$ for my resource scheduling problem, which I mapped into a graph problem. Processes $P_i$ need resources $R_i \in ...
2
votes
0answers
330 views

Reconstructing an optimal Simplex tableau from an optimal solution

I have here a bounded LP with infinite optimal solutions: ...
3
votes
2answers
59 views

Determine the equations needed to solve a problem

I am trying to come up with the set of equations that will help solve the following problem, but am stuck without a starting point - I can't classify the question to look up more info. The problem: ...