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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").

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Multi-objective optimization.

If we want to optimize two characteristics of a result lets say Accuracy(maximize) and RMSE(minimize) simultaneously using an evolutionary optimization technique, how will the update condition work in the optimization algorithm? In single-objective…
StormClouds
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Mathematical generalization of the equilibrium point

Let $U$ be an open set $U \subset \mathbb R^n$. Let $f$ be a class-2 function $f: U → \mathbb R$. Prove or disprove the following statement. $∇^2 f=0$ and $∇f= 0$ at $x_0 \in U$ implies $x_0$ is the saddle point.
Chris kim
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What is a feasibility cut in Benders decomposition?

I am currently learning about solving problems with iterations, and my text states that: At every iteration a violated optimality or feasibility cut is found and added to MP I am however quite lost to what is meant by that.
Jakob Jakobsen
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Which Method to use for small unconstrained optimization problem?

I have a loss function which I want to minimize. That function depends on 4 variables, which need to be tweaked to find the minimum. There is no need for finite differences, because I know the analytical function. The function is non-convex, but in…
horsti
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What score-assigning function would maximize this desired shape?

Let's say I have a setup where an agent places blocks into bins in such a way as to maximize its "score". The score is a function of the number of bins filled and the number of blocks in each bin. The bins are automatically sorted largest to…
Anthony Khodanian
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Minimization of $xA + \sqrt[x]{s}B$??

Let $x$ be a variable (positive integer), and $A, s, B$ constants. Then I want to know the way to minimize $xA + \sqrt[x]{s}B$. How can we solve it? All of $A, B, s$ are positive integers. The following conditions hold $A > B$ and $ x < s$.
mallea
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Decomposing an optimisation problem

Take the following optimisation problem $$ (*) \hspace{1cm} h(u_1,u_2,u_3)\equiv \min_{p_1,p_2,p_3} \sum_{j=1}^3(f(u_j,p_j))^2\\ \text{s.t. } g(u_j,p_j)\leq b_j \text{ }\forall j \in \{1,2,3\}\\ $$ where $u_j$, is an $m$-dimensional vector of real…
Star
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Are inequalities continuously differentiable functions?

My textbook describes smooth optimization problems as "problems where the objective function and constrains set are represented using continuously differentiable functions". Then for example, if I have a problem with the constraint set x ≥ 0, y ≥ x,…
judie
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Optimize ray path going through an axis aligned box

I'm confronted with a problem in which I must minimize a travel path going from some transmitter $T$ to a receiver $R$, going through an interface -- i.e. a change in velocity causing refraction -- and having to pass through a point P of an axis…
TheCoconutChef
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Optimization Problem Help- Purchasing

I posted this problem the other day on the forum and am currently completely stumped on how to proceed. Purchasing Optimization Problem I have coded this problem in R with the data that this information is from such that the objective function does…
tfr950
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vector derivative of vector summation

Want to find, $$ \frac{d}{dV} \sum_{k=1}^{n} {V_{k}}^{2} $$ Where $V$ is a $n$-dimensional vector. Is following correct? If not then what is the answer? Let $$ V = [v_{1}, v_{2}, v_{3}, \dots , v_{n}]$$ $$ \frac{d}{dV} \sum_{k=1}^{n} {V_{k}}^{2} =…
Ajey
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I need to optimize a linear programming problem of a manufactoring company

A manufacturing company has a set $I = \left \{ 1,2, ..., i, ..., M \right \}$ of $M$ iron ore reduction factories. In each of these reducing factories the mineral is proccesed, producing a set $J = \left \{ 1,2, ..., j, ..., N \right \} $ of $N$…
IGNACIO ZANETTA
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A variant of Knapsack Problem in $L^1$ functional space

Given $L^1$ functional space $V=L^1([a,b])$ and a positive real number $B$. Let $\varphi$ and $g$ be continuous functions defined on $[a,b]$ such that $\varphi(x)\geq 0$ and $g(x)\geq 0$ for all $x\in [a,b]$. Consider the following optimization…
Leonard Neon
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The Range of Taxi Fares

You are in the back of a NYC taxi, and know exactly how fare your trip was in miles (m), and exactly how long it took in hours (t). The taxi driver gives you bill, but you want to make sure they've charged you correctly. You know that taxi fares are…
Cameron Chandler
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Optimization Problem, no numbers?

A company wants to encrypt a document containing important passwords. To do this, the product of a positive integer and a negative integer will need to be minimized. If the positive integer is 11 greater than the negative integer, what is the…
Ayanoria
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