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Question Does a transformation of the following problem to convex optimization exist? \begin{aligned} \label{1} \min_{\vec{x}, \vec{y}} \quad & F(\vec{x}, \vec{y}) \\ \textrm{s.t.} \quad …
asked Jun 21 '21 by Qurious Cube
1
vote
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) & …
answered Jun 26 '21 by Qurious Cube
2
votes
Binary (Boolean) values are integer values. Therefore, optimization problems with boolean constraints are either integer programming or mixed integer programing (MIP). Generally, there is no easy algo …
answered Jun 27 '21 by Qurious Cube
4
votes
0answers
Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount …
asked Jun 13 '21 by Qurious Cube
1
vote
For timing within the gurobi solver, maybe you can call <optimizer>.solve() method with report_timing=True, as described in pyomo's documentation at https://pyomo.readthedocs.io/en/stable/library_refe …
answered Jun 28 '21 by Qurious Cube
1
vote
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
2
votes
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
3
votes
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
2
votes
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
0
votes
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
3
votes
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
3
votes
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
8
votes
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
2
votes
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
4
votes
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: $$ …
asked Aug 21 '21 by Qurious Cube