# Questions tagged [unconstrained-optimization]

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### How to exponentiate binary variables in QUBO-type problems?

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 ...
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### Inverse Ising problem

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 ...
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### How do I transform the number partition problem into QUBO form

In this article A new modeling and solution approach for the number partitioning problem1, it transforms the number partition problem into a QUBO form like equation (2.1) on page 2. \text{diff}=\...
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### How to define the upper bound for a binary expansion of a slack variable in Quadratic Unconstrained Binary Optimization (QUBO) models?

I've recently started to study how to formulate optimization problems as QUBO models through this paper/tutorial: https://arxiv.org/pdf/1811.11538.pdf One of the steps is to transform the inequalities ...
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### Trouble implementing a line-search algorithm

I am trying to implement a simple line-search algorithm in Julia. I am new to Julia programming, so I am learning it on the go. I'd like to ask for some help, if possible, to correct an error while ...
I am minimizing $f(x_1,x_2) = 100(x_2-x_1^2)^2 + (1-x_1)^2$, where I try many algorithms to compare with each other. All of the algorithms find the optimal solution $(1,1)$ quickly, so I am not ...