# Questions tagged [discrete-optimization]

For questions about optimizations involving variables which can only take on a discrete set of values (e.g. integers, points on a lattice)

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### Linearize problem with absolute value

Is there any method to linearize the following optimization problem? \begin{align} min_{x,y} &~~ c~[x; y] \\ st &~~ \sum x\leq \alpha_1 \\ &~~ \sum |y|\leq \alpha_2 \\ &~~ \sum y= 0 \\ ...
1 vote
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### Help with CVXPY and Disciplined Convex Programming

I'm trying to recreate Figure 1 in this paper. This requires maximizing equation (19), which I have convinced myself is concave, but I am having trouble implementing it in CVXPY. Here is the code I ...
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### 'Items in a bucket' optimizaiton problem?

Sorry for question's silly tittle. I don't quite know how to name my problem, that's why I'm here. Imagine you wish do add the collumns of you data ('1','2','3'...'30k' etc.) in such a way as to ...
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### Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
11 views

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### What is this discrete optimization problem called?

It feels like this problem should be commonplace, but I don't know what it's called: Minimize $$\sum_{i=1}^{n}a^{(i)}_{k_i} + \sum_{i=1}^n\sum_{j=i+1}^n b^{(ij)}_{k_i k_j}$$ with respect to ...
69 views

### Given a list of intervals, find region that is contained by the largest number of those intervals

Start with 1d case. Say I have lots of 1d intervals $[s_i, e_i]$ and I want to find an interval $[s^*, e^*]$ to maximise the count of interval $i$ such that $[s_i, e_i]\supseteq [s^*, e^*]$. 1d case ...
909 views

### Constrained simulated annealing

Simulated annealing is a useful technique for finding near-optimal solutions to combinatorial problems. I have found a lot of tutorials on implementing the basic algorithm, but miss a general guide as ...
419 views

### Knapsack problem with fixed number of elements?

I am looking at an optimization problem that looks like this:  \text{minimize}\;\; \mathbf{x}^TQ\mathbf x \;\;, \; \mathbf x \in \mathbb R^n, x_i \in \lbrace 0, 1 \rbrace\\ \text{subject to}\;\; ||...