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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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Are there any standard methods to solve a linear objective with nonconvex constraints?

I see that nonlinear programming entails nonlinear objectives with convex or linear constraints. Is there any theory/method to solve linear objective with nonconvex constraints and some convex constraints?
sprajagopal
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solve the equation $c_1+c_2 e^{c_3 x}+e^{c_4 x}-e^{c_5 x}=0$

How can I solve the equation $$c_1+c_2 e^{c_3 x}+e^{c_4 x}-e^{c_5 x}=0,$$ where $c_1,\ldots,c_5$ are real numbers? I encountered this equation when I was solving a maximization problem. i can say only that all $c_i$s are real x is positive and i…
Harish
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About a step in the derive of Netwon Method

I do not understand a step in the derive of Newton method in my lecture notes: When it applies derivative on both sides of $q(x) = f(\bar{x}) + \bigtriangledown f(\bar{x})^{T}(x-\bar{x}) + \frac{1}{2}(x-\bar{x})H(\bar{x})(x-\bar{x})$ Should not it…
nam
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Optimization Problem of Two Variables, One Dependent

I am actually working on a program of sorts. This program takes a user entered value that specifies how many white keys they can span with one hand on a piano. It then computes (based on research) the general reach from one finger to the next one…
Jarrod Christman
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Min and max of a product.

Let $x_i\in X_i\subset \mathbb{R}$ so that each $X_i$ is a compact set with no isolated points for all $1\leq i\leq n$. Let: $a_i\in X_i$ so that $|x_i|\leq|a_i|$ for all $x_i\in X_i$. $b_i = \max\lbrace x_i \in X_i\rbrace$. $c_i = \min\lbrace x_i…
Darth Geek
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Global Maximums and Minimums

My book states: "It is also true that if $x^*$ is an interior point and: a global maximum of $f$ , then $d^2f(x^*)$ is negative semi-definite. a global minimum of $f$ , then $d^2f(x^*)$ is positive semi-definite. But, it is not true that if $x^*$…
Peter Pan
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Constraineed Maximization Problem

I am creating a game, and have run into quite a tricky problem which I have been wrestling for days. I have been able to turn into somewhat mathematical terms (bare with me, I'm a programmer not mathematician) -- but I am no closer to a…
Heptic
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Optimum set partitioning with constraint

Be $A \subset D \wedge m \in D \wedge \forall x \in A:x < m$, with $D$ finite and included in the positive integers, I need to partition $A$ into $B_n$, while minimizing $n$, so that $$\left(\sum_{i\in B_n}i\right) \leq m$$ I also know that $\max(A)…
Ismael Luceno
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Optimization, multivaraible

I have a question regarding multivariable optimization. In particular, I have a function f(x,y,z,w) and I want to maximize f in terms of x only (with other variables treated as parameters). Also I have one more constraint: y=g(x), that is, this…
kou
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Gradient descent in inequality constrained optimization problems

I want to solve an optimization problem using a gradient descent algorithm maximize $$ max \log( \frac{Ax + b}{ Cx + b} ) $$ $$s. t. \quad 0 \le x \le 1 $$ where x is a vector and the inequalities are component-wise (i.e. all the elements of x…
user164999
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Solving a optimization problem

Here is the objective function of my optimization problem: $$ \min \left( \sum_{i=1}^{n}a_i(1 - X_i)\right), \qquad n = \arg \min(X_i = 1) $$ $$X_i = \{0,1\} \text{some other linear constraints} $$ Does anybody know: Is it a linear…
Wenjie
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Find maximum of the function

I have the following target function $$ f(m,q)=\sum^{N}_{i=1}|m_i-q_i| $$, where $$m,q\in R^N$$ and $$\sum^{N}_{i=1}m_i=1, \forall m_i>0$$ $$\sum^{N}_{i=1}q_i=1, \forall q_i>0$$ I would like to find such vectors $$q,m$$ that deliver maximum of the…
Taras Murzenkov
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How do I know if I have imaginary numbers when using Newton Raphson Method?

I am studying Newton-Raphson Method but I am facing questions in my head. As far as I know Newton Raphson Method works on real values, but what if Newton Raphson Method faces an imaginary number when it is find real values on x-axis? and What to do…
user122358
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How to find the global minimum or maximum of a data set

From some experiment, I am getting noisy data. I am interested in highest maximum value from data. Somehow data is periodic and I want to get the highest maximum value from first period. I am quite new in this area, Please suggest me any reading…
User1551892
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Need help with second derivative test

In an optimization problem with restrictions, when I have already found the critical points of a function and I have to classify those points (they can either be maxima or minima or saddle points), do I have to analyze the hessian matrix of the…
Werther
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