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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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What is the most efficient way of determining a date of birth using yes/no questions?

First question here on StackExchange! Sorry if this question is not quite of the correct style - please let me know if so. Anyway, here's the context. I'm trying to write a program to determine a date of birth (not the year, just the day/month) in…
Cathal
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How to transform equivalent optimization problems

Can somebody either explain how to show the equivalence of the three alternative optimization problems in MPT (or point me to some literature)? I am looking for the necessary "algebraic steps" if at all possible rather than the intuitive explanation…
Marvin
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Function Maximization

Good day. I have no idea how to solve the following question and will be grateful for any help. Suppose we are given $~n~$ real numbers $~y_1,...,y_n~$. Is there any simple way to minimize function $~f(y) = \sum_{k=1}^{n}|y_k-y|$ ? Thanks in…
Igor
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Maximum of $A^tB^{1-t}$

What is the maximum of $A^tB^{1-t}$ for positive $A$ and $B$ and for $t \in [0,1]$. I think the maximum occurs at end points either $t=0$ or $t=1$, right?
Boby
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Independent variables in optimization

I'm not sure whether I'm asking very obvious/stupid question, but essentially I'm looking for references. I am looking for the notion of independence in the context of optimization problems (I am doing LP with disjunctions over reals, but that…
cheshire
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Problems of choice with immediate effect under conditions of uncertainty

A farm, in order to commercialize a product, may select between two intermediaries, which offer the following conditions: A) A fixed cost of 2000 dollars for any level of production; B) A variable cost equal to 10% of revenue. Each kilogram of…
Ottavio Spadaccini
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Check my solution for optimization problem

A piece of wire 40 units long is to be cut into two pieces. One piece will be bent to form a circle; the other will be bent to form a square. Find the minimum and maximum values of the area. I found that $$Area(x)=\left(\dfrac…
user181609
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Is there any standard way to handle fractions of bilinear constraints in optimization?

By fractional bilinear constraints, I mean this form: $$\frac{a_1 + a_2 + a_3 + \cdots}{b_1 + b_2 + b_3 + \cdots} \frac{c_1 + c_2 + c_3 + \cdots}{d_1 + d_2 + d_3 + \cdots}$$ Here, $a,b,c,d$ are variables of the optimization.
sprajagopal
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How to approach a minmax problem?

Starting with a certain geometric problem, I have reached this function: $$R(s,t,u,v)=\max(s-u,s+u,t-v,t+v,sX+tY+u, tX-sY+v)$$ where $X\geq0$ and $Y\geq0$ are parameters. I have to find the minimum possible value of $R$ given the paramters,…
Erel Segal-Halevi
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minimize expression

How can the following expression be minimized wrt w: $$ \frac{w^T D w}{w^T S w}, $$ where $w \in \mathbf{R}^n$, $D \in \mathbf{R}^{n \times n}$ symmetric, and $S \in \mathbf{R}^{n \times n}$ symmetrix positive definite. Please give me some hints…
Tom
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multivariate piecewise-linear equality constraint in optimization problem

I have an optimization problem of the type: $\min f(x) \\ s.t. Ax \le b \\ g(x)=0 $ where $g(x)$ is a piecewise-linear function defined as: $g(x) = \begin{cases} c_1^Tx & \text{if $x_1+x_2-x_3 \ge 0$} \\ c_2^Tx & \text{otherwise} \end{cases} $ I…
giulatona
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How to write such a constraint?

I have the following constraint that I need to write in an optimization problem but I failed to do it. Let $x_{ij}$ be a binary variable. So that: $$ x_{ij} = \begin{cases} 1, & \text{if $i$ and $j$ are in the same group}\\ 0, &…
Chiba
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Optimization for nonlinear function with linear constraints

I am trying to come up with nice solution for a specific RCPSP. Context There is a small factory which can produce P kinds of products on N machines each machine is universal but can only create one kind of product in one setting. The machine…
jakub.petr
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Optimization with probabilities

How does one take care of constraints when setting up an expected returns maximization model of the following kind: $y=f(x-r)$ if $z > a$, $z=g(x-s)$ if $w>b$. I want to max $E=prob\times y + (1-prob)\times z$. Without the constraints, the first…
user172310
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minimax vs max-min

I am a beginner in optimization and I have the following questions: First question: is there a difference between the two optimization formulations? OP1: $\max_{x} \min_{k} g_k=f(x)$ and OP2: $\max_{x} \min_{k} G=f(x,k)$ I think there is a big…
Noor
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