# 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.

13,227 questions
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### coordinate descent in very basic

I try to figure out how coordinate descent works from wiki https://en.wikipedia.org/wiki/Coordinate_descent From wiki example : the equation is $5x^2-6xy+5y^2$. Let $x = -0.5$ and $y =-1$ For the ...
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### zdt4 test function [on hold]

please help me to run this code in Matlab: message error :Caused by: Failure in initial fitness function evaluation. GAMULTIOBJ cannot continue. ...
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### Optimization of the least used wire

question:There are two trees that are spaced 30 meters apart. The height of one of them is 12 meters and the other is 28 meters. The two trees should be kept by two wires so that both wires are ...
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### How to optimize a series of equations whose outputs are a variable of the subsequent equatinos

The basic question is, given $f(x) = y$ and $f(y) = z$, how can you find $x$ such that $z$ is at its maximum? I can optimize each equation independently, but I do not know how to optimize when ...
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### Procrustes Problem with Maximization (Instead of Minimization)

The classical (orthogonal) Procrustes problem is to solve the optimization problem $$\begin{array}{rl} \min&\|\Omega{A}-B\|_F\\ \text{s.t.}&\Omega^\mathrm{T}\Omega=I \end{array}$$ The ...
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### Find the minimum and maximum possible values of the conditional probability

Given two events $A$ and $B$, such that $P(A) = 0.3$ and $P(A ∩ B) = 0.1$. Find the minimum and maximum possible values of the conditional probability $P(A | B)$.
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### Permutative Constraint on Image Approximation

Motivation I am trying to explore the idea of constraining the approximation of an image represented by an $m$-by-$n$ matrix $A$ by the values on a linearly-spaced interval of $mn$ elements $L$ ...
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### Coming up with a cost function for optimization for a complex control system

I am relatively new to this topic. I understand the basics of optimization of control systems using a cost function and constraints and solve it as a minimization or maximization problem. I also ...
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### mixed integer programming - turning conditional statements into inequalities

I have if statements in my constraints and I'm having trouble turning it into an inequality problem. The statement is as following: IF a>=x1, THEN f(x1,x2) = a+x2, Else f(x1,x2) = a. x1 and x2 are ...
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### Steiner tree to minimise travelling distance: Building roads to connect a network of points

Suppose we have four points in a unit square, as described in the question here. We are tasked with building a network of roads that connect all the cities. The travelling distance (T) of this network ...
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### Finding a constraint on one variable of a multivariable function to constrain the entire function

I have a function. L(x,y). L(x,y)= 8.5(xy) -3(x+y) + 1. Now I want to let my variables only take values between 0, and 1. The problem is as follows. For what values of Y, is L(x,y) < 0. That is, ...
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### Maximizing Area of a quadrilateral inside of a square

The square ABCD has point M located on side AB and point N on side CD. Lines CM and BN intersect at point U. Lines DM and AN intersect at point V. Determine where points M and N should be placed to ...
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### Finding out maximum value of a multivarivable function with inequality constraints.

If x,y and z are 3 uniform random variables within [0,2pi) and |x-y| is bounded between 60 and 150 degrees,then what shall be the maximum value of F(x,y,z) =(c1/c2)^2, given c1 equals cos(x-z) and c2 ...
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### Optimization without complex numbers

We need to find a minimum of functions: (1+$\sqrt x$)$^2$+$y^2$ Due to the fact that the function has a square root, the optimization algorithm goes into the area of complex numbers. How to make so ...
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### integer programming???

I have a math problem and I would like to solve it, but I'm not sure what area to look under. Basically given $x \in \mathbb{R}^k$ (for my purposes, $x \in \mathbb{Q}^k$ since I am using a computer) ...
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### Dual of conic program

Let $A$ be an $m \times n$ matrix (over $\mathbb{R}$), $b \in \mathbb{R}^m$, $c \in \mathbb{R}^n$ and $K \subseteq \mathbb{R}^n$ is a closed, convex, pointed cone with non-empty interior. We define a ...