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Questions tagged [unconstrained-optimization]

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4 votes
2 answers

How to approximate an uncertain constraint?

Suppose $\theta$ is the uncertain vector of parameters and it varies within the interval $\Theta$. We have the following uncertain constraint. $$ \sum_{i} f_i(x,\theta) \ge \sum_{j} g_j(x,\theta) \...
Amin's user avatar
  • 2,140
3 votes
1 answer

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 ...
Qurious Cube's user avatar
7 votes
2 answers

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 ...
Qurious Cube's user avatar
3 votes
1 answer

How do I arrive at the form given in this paper, for the QUBO version of the number partitioning problem?

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}=\...
Steve Deltora's user avatar
4 votes
1 answer

Why are the bounds 3 and 6 instead of 7, in this binary expansion of a slack variable in this QUBO problem?

I've recently started to study how to formulate optimization problems as QUBO models through this paper/tutorial: One of the steps is to transform the inequalities ...
Felipe Toledo's user avatar
0 votes
1 answer

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 ...
Quasar's user avatar
  • 203
8 votes
1 answer

Speed of convergence for minimizing Rosenbrock's function

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 ...
independentvariable's user avatar
11 votes
1 answer

Armijo Line Search Parameters

I am trying to compare many unconstrained optimization algorithms like gradient method, Newton method with line search, Polak-Ribiere algorithm, Broyden-Fletcher-Goldfarb-Shanno algorithm, so on so ...
independentvariable's user avatar