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Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

22512 questions
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Finding x which maximizes the volume of any cuboid missing one side

So my grandpa and me where doing some maths for fun and we stumbled upon this problem: Given a rectangle with unknown sidelenghts a and b, we need to cut off a square in each corner (call the side length of the square x) so that we get a net of a…
user1008730
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Minimization problem of norm

I trying to solve optimization problem $\min\underset{x \in C} f(x) = \| x - 1\|^2_2$, where $C = \{x \in \mathbb{R}^3 | x_1 + x_2 + x_3 = 1, x_1 > 0, x_2 > 0, x_3 > 0\}$. What I did: I found Lagrangian of $f$: $$L(f) = \frac{1}{2}\|x - 1\|^2_2 +…
LightM
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Armijo's algorithm returns a value of alpha too small

We've been working in class on optimization methods, and were asked to implement a quasi-Newtonian algorithm to find the minimum of the function: $f(x, y) = x^2 + y^2$ using the David-Fletcher-Powell method to approximate the hessian of $f$ and…
Omar El Atyqy
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Which nonconvex problems can be solved optimally?

I was recently wondering for which common nonconvex problems we have algorithms that are guaranteed to find optimal solutions. The only one I could think of is the singular value decomposition. Are there other nonconvex problems we can solve…
Dr Waluigi
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Solution of Projected Gauss-Seidel

I'm using a method that is giving satisfactory results in practice, but I have a hard time trying to formulate rigorously what I'm actually computing. I'm solving an optimization problem using Projected Gauss-Seidel algorithm and I would like to…
duburcqa
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An assembly line problem

suppose there is one workstation of interest at an assembly line in which a product stays for a few hours and is processed by the operators there before moving to the next station. At the station there are several operators op = {op_1, op_2, ...,…
Sebastian E
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KKT conditions for minmax optimization

If I have a function of the form $V(x,y) = x^2 + y^2$, and I want to perform $min_ymax_xV(x,y)$, given the constraint $x^2=1$, how can I write the KKT conditions to solve this problem? Thanks
novelnow
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How to caculate Lagrange multipliers with gradient method

I was working my final year project, and it was basically a replication of a past paper. So when I was working on the optimization part. I was a bit confused about some concepts mentioned in that…
Yanbo Liu
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How do I minimizie cost of charging an electric car?

I want to find a charging schedule that minimize cost of charging an EV. The main objective is to have a fully charged car for the next morning, but the sub objective is to minimize cost based these two things combined: Charge when electricity is…
NorwegianClassic
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Calculate the highest possible chunk size

I need to find the higest possible value to multiply with in the following senario. I have a collection of items, all items are of the same type and thay have a fixed number of columns. The problem is that i need to find out what the higest possible…
user83571
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Efficient criteria for peak picking

I have two arrays like red = np.array([0.3, 0.4, 0.3, 0.3, 0.6, 0.3, 0.3, 0.7, 0.8, 0.7, 0.4, 0.5, 0.6, 0.6]) blue = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2, 0.6, 0.9, 0.6, 0.2, 0.2, 0.2, 0.2]) The desired result is red_out = np.array([0.0,…
Stepan
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Maximum value of the vandermonde polynomial

Let $n$ be an integer greater than 1. How must $n$ numbers $a_i$ in the interval $[0,1]$ be chosen that the vandermonde polynomial $$\prod_{i\ne j} (a_i-a_j) $$ has the maximum possible value ? My conjecture, that the numbers must be equidistant,…
Peter
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Optimisation problem - Knapsack dependent item selection

I think this is a take on a knapsack problem but I'm struggling to find an example similar: Say I have various tubes filled with red balls and black balls. The balls are contained in the tubes so that they cant move around and to remove a ball you…
Bronwen Edge
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Include the triangle with the least sum of squares of the sides in the circle.

"Include the triangle with the least sum of squares of the sides in the circle." Use Lagrangian $$L = ((x_{1}^1 - x_{1}^2)^2 + (x_{2}^1 - x_{2}^2)^2) + ((x_{1}^1 - x_{1}^3)^2 + (x_{2}^1 - x_{2}^3)^2) + ((x_{1}^2 - x_{1}^3)^2 + (x_{2}^2 -…
spiral_being
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Loss Function and Probability

Suppose we have some input variables and the output variable is categorical. So the output $G(X)$ can be in one of $k$ classes. Therefore an estimator $\hat{G}(X)$ will also be in one of these $k$ classes. Let $L$ be a $k \times k$ matrix with…
optguy
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