# Questions tagged [constraints]

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

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### Calculating a maximum size of subset of permutations and finding an example of such subset. [closed]

I've been trying to solve a problem of finding a subset of permutations under a certain constraint. So far I wasn't able to solve this, hope someone can help. Thank you in advance. The problem: We ...
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### How to maximize the geometric mean? - SLSQP would be correct?

I am trying to find a set of weights for each asset in the portfolio, that would give me the highest geometric mean, with only the constraint that all weights must sum up to 1. I'm currently using the ...
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### Number of Combinations for Patients and Hospitals

I thought of the following problem. Suppose medical patients can have the following characteristics: Smoking Status: Often, Never, Sometimes Weight: Overweight, Underweight, Healthy Age: Child, ...
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### Model Predictive Control with integral (end-of-horizon) constraints

Let $\mathscr T = \{0,1, \ldots, T\}$ denote the entire time horizon, $x : \mathscr T \to [0,1]$ the state and $u : \mathscr T \to \mathbb [0,1]$ the control. Consider the following problem: \begin{...
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### Optimization Algorithm for Continuous Objective but Binary Nonlinear Constraints

Is there an derivative-free local optimization algorithm for a continuous function with nonlinear constraints, where the constraints are binary? In other words: $$\max_{x \in \mathbb R^n} f(x)$$ ...
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### How to understand this Local Minimizer solution?

I have the following problem : Let $f: \mathbb{R}^{2} \rightarrow \mathbb{R} ; f\left(x_{1}, x_{2}\right)=5 x_{2}$, let $\Omega=\left\{x \in \mathbb{R}^{2}: x_{1}^{2}+x_{2} \geq 1\right\}$, and ...
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### How to bundle pairs of trips?

I have a database of real-time trip demands: ...
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### Speed adjustment on a given path for cost minimization with fixed departure and arrival time

I have an optimization problem which consists in going from a departure point to an arrival point given a set of predefined intermediate points between the departure and the arrival. The departure and ...
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### Solve the minimization problem using subdifferentials on a non-differentiable continuous function subject to two constraints

This is a desmos plot of the problem I am exploring: https://www.desmos.com/calculator/0rxekqcj26 My first question is how to find the subdifferential of $f(x,y) = \max\{|x|, y + 4\}$. From my ...
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### Range of z for convex constraint?

What would the range of z be if this were to be a convex constraint? $2x_1^2 + (2+z)x_2^2 - x_3^2 \leq 5$ I thought it could be approached by applying the two conditions of a convex hull (i.e, the ...
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### Linear Programming- Three products, four workshops, and a limited supply of unique components.

Say I have three products, 1, 2, and 3. There are four workshops (A,B,C,D) that build these 3 products. Product 1 must be processed in workshops A and B Product 2 must be processed in workshops A and ...
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### Linear Programming- A shipment of three products in a cargo plane.

Suppose we want to maximize revenue in the following situation. We have 3 shipments of products. Shipment one: ...
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