Mathematics Stack Exchange
Mathematics Stack Exchange

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
0
votes
0 answers

Least Squares Method for two varying parameters

I wonder if someone could show me some pointers with regards to the following query. I have the following constraint: $$ b_{min} \leq b \leq b_{max} $$ these values are used to generate a value for x: $$ x = f(b) $$ So I have a range of values for…
Mike
  • 461
0
votes
1 answer

branch and cut optimal solution guaranteed

Is "Branch and cut" method guaranteed to obtain an optimal solution? if not, under what conditions it would be guaranteed. is there a reference that I could refer to (a paper would be great)? thanks
A. Shokair
  • 35
0
votes
1 answer

solution to optimization problem

For the problem: $\min {x_1}^2$ subject to $x_1 \leq -1$ and ${x_1}^2 + {x_2}^2 \leq 2$ The possible solutions are: $(x_1,x_2)= (-1,0)$ and $(x_1,x_2)= (-1,-1)$. The optimal value is $1$. Are these solutions correct? If yes, can I include both of…
Jyothi Jain
  • 41
0
votes
3 answers

Optimization with Boundary Solutions

I am trying to maximize this objective function $$f(x)=-x^2$$ subject to $1 \le x\le 3 $ This is the Langrangian I wrote: $$\mathcal L (x, \mu, \lambda) := x^2 + \lambda (3-x)+\mu (x-1)$$ F.O.C + other conditions 1) $2x=\mu-\lambda$ 2) $\lambda…
jessica
  • 1,002
0
votes
2 answers

Optimization Problem with Fence

Question: A 5,000 m² rectangular area of a field is to be enclosed by a fence, with a movable inner fence built across the narrow part of the field.The perimeter fence costs $10/m and the inner fence costs $4/m. Determine the dimensions of the field…
Guest Man
  • 95
0
votes
2 answers

How to invert an exponential weighting

I am sure that this question has been asked before, but what is the solution of $y_i = \frac{e^{x_i}}{\Sigma_{j=1}^{n} e^{x_j}} \forall i $? i.e. how does one make $x_i$ the subject?
tangerine
  • 51
  • 5
0
votes
1 answer

Why is this set bounded?

teacher said that this set is bounded without any elaboration,to me it is not obvious that it is bounded,in fact i think that it is unbounded and now i am confused. $$S=[{(x,y,z)\in R^3}|x\geq 0,y\geq 0,z\geq 0,x+y+z=2]$$ Now this is a plane in the…
DrStrange
  • 116
0
votes
1 answer

Optimization the cost of fish tank

I am trying to minimize the cost of the fish tank. The cost of the tank is depending on the thickness of the tank. The shape of tank is a cylinder without a top. The tank is going to have a volume 250 gal. If the tank height is greater then 24 in.…
MikeJ
  • 1
0
votes
1 answer

Optimal solution for problem with multiple conditions

Please suggest an algorithm or some direction to look into, to find optimal solution for the following problem: Given n finite sets (of size at most 8) of natural numbers $V_i$ , choose only one $x_i$ from each set that will satisfy the following…
Denis
  • 1
0
votes
0 answers

Optimization of a piece-wise smooth function

I'm working on a problem that involves finding the global optimum of a function that looks like: $U = \lambda\cdot u (x)+(1-\lambda)\cdot u(y)+V(a,b)$ I need to find values for $x$, $a$ and $b$ ($y$ is pinned down by an additional constraint) and…
Tim
  • 1
0
votes
2 answers

Optimization triangular prism

I am working on a math project on optimisation and have a triangular prism (tent) with a given volume of 2.8 cubic meters. The "top" of the tent is out of a water-resistant material for 2.25 dollars per square meter, and the floor material costs…
Conny Schneider
  • 3
0
votes
1 answer

local minimiser of a subset is a local minimiser of a set

Suppose $ x^*$ is a local minimiser of $f$ over $\Omega$ , $\Omega \subset \Omega ' $, $x^*$ is interior point, how to prove that $x^*$ is also local minimiser over $\Omega '$. It looks obvious, i try to show that the neighbourhood of $ x^*$ is…
Karusmeister
  • 117
  • 4
0
votes
2 answers

Lagrangian and optimization

I am using the lagrangian to find the minmum of the function: min f(x₁,x₂)=1/(3+x₁)+7/(2+x₂) s.t x₁+x₂=4 Then the lagrangian is L(x,λ)=1/(3+x₁)-λx₁+7/(2+x₂)-λx₂+4λ I am stuck at this point because the standard method for solving grad L is…
Johnny Byr
  • 35
  • 5
0
votes
0 answers

How to find a mathematical relationship between $x$ and another variables such that $y$ is a minimum?

Consider the expression $$y=\frac{1375\times44.5}{x}+\frac{1375}{7−0.1(x−110)−0.05n}\times1.49$$ where $n$ are integers between $0$ and $10$ to keep it simple. How do I find the relationship between $x$ and $n$ such that $y$ will always be a…
Son Jerm
  • 9
0
votes
1 answer

Minimize the expression $4x^2+(x+2y-6)^2+16y-23$

Let $x$ and $y$ be real numbers. Find the smallest possible value of $4x^2+(x+2y-6)^2+16y-23$. What method should I use?
Ray Cheng
  • 101
1 2 3
…
97 98