Search Results

Results found
Search options user 5705
15 results
Minimize $x^2$ where $1 \le x \le 2$. \begin{aligned} \min_{x} \quad & f(x)\\ \textrm{s.t.} \quad & h_{1}(x) \le 0\\ &h_{2}(x) \le 0 \\ \end{aligned} where \begin{align} f(x) &= x^2 \\ h_{1}(x) & …
Here is a small variation of RobPratt's answer. I will use two sets, as an example. Two sets of constants are given: $S_1 = \lbrace x_{1,1}, x_{1,2}, x_{1,3} \rbrace$ and $S_2 = \lbrace x_{2,1}, x_{2, … answered Jun 30 '21 by Qurious Cube 0answers I can explain why Lagrange multipliers work for scalar functions by vector calculus. Consider optimizing$f(\vec{x})$subjected to the constraint$g(\vec{x}) = c$. At the optima, we can move infinites … asked Jun 30 '21 by Qurious Cube Maybe this can work? Numbering is same as sorting. Disregard the layers and treat the whole thing as a single graph. Use Cuthill-Mckee (if the bandwidth is low) or other heuristics for the graph bandw … answered Jul 1 '21 by Qurious Cube Treat nodes in 1st and 3nd layer as extra edges in the 2st layer to make a merged layer. Minimize bandwidth of 2nd layer. Repeat for the other layers. layer 2: o o o \ / \ / layer 1: @ … answered Jul 2 '21 by Qurious Cube Transform the optimizing variables$x$and$y$in everything (the whole model) to$u = \frac{ax}{\ln(b + cy)}$and$v = x$Transformed constraint$u + dv \le A$is linear. Therefore, the transformed c … answered Jun 20 '21 by Qurious Cube 1answer Ising Model In an Ising model, the Hamiltonian of one configuration of spins$\vec{s}$is: $$H(\vec{s}, \mathcal{J}, \mathcal{h}) = \sum_{i} h_{i} s_{i} + \sum_{i \ne j}J_{ij} s_{i}s_{j}$$ where eac … asked Jul 24 '21 by Qurious Cube According to the equality constraint (the equal to 4 one), at least two of the$x_{?}$are 1. Therefore, the slack for the 1st constraint is at most 3. According to the equality constraint, the worst … answered Jun 20 '21 by Qurious Cube 2answers Inverse Ising Problem The inverse ising problem means fitting the coupling$J_{ij}$and field$h_{i}$parameters given a sample of configurations of spins. Each spin$s_{i}is either +1 or -1. The Ha … asked Jul 24 '21 by Qurious Cube 0answers How to solve minimax mixed integer problem with a large high dimensional feasible region? \begin{aligned} \max_{\vec{x}}\min_{\vec{y}} \quad & \vec{r} \cdot \vec{x} + \vec{s} \cdot \vec{y}\\ \textrm{s … asked Jun 29 '21 by Qurious Cube 1answer How to solve the following minimax problem quickly? The variables are all continuous. $$\max_{x_{1}, x_{4}, x_{5}} \min_{x_2,x_3} \vec{c}^{\intercal} \vec{x}$$ subject to the following constraints:\$ …