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
1 answer

What is the optimal of inventory optimization of the following case

What is the optimal of inventory optimization (one inventory in serial system) when considering fixed ordering cost, and (holding/units)cost and (shortage/units)cost
user10296606
  • 111
0
votes
0 answers

Can a function be neither concave nor convex?

I have a function of $f(x)=x^5+x$ on the interval $[-2,2]$. By using the first order derivative method of convexity we have $f(x) ≥f(x_0)+∇f(x_0)^T(x-x_0)$ and on the right hand side I get $-4x_0^5+5x_0^4+x$ from which we can't tell whether it's…
Nick202
  • 149
0
votes
1 answer

If the sum of two functions is convex is at least one of them also convex?

I know that the sum of two convex functions $f$ and $g$ is convex, but can we also state the opposite? If the sum $f+g$ is convex, does it mean that at least one of them is convex?
Nick202
  • 149
0
votes
1 answer

How is the minimization part done in projected gradient descent?

How is the minimization part done in projected gradient descent? It says to do: $$y_{k+1}=x_k-t^{(k)}\partial f(x^{(k)})$$ where $x_{k+1}=\min_{z \in \chi} \|x-z\|$ So is one supposed to solve the $x_{k+1}$ using some other minimization method? Or…
mavavilj
  • 7,270
0
votes
1 answer

How to use the barrier method for equality (or positive) constraints?

How to use the barrier method for equality (or positive) constraints? https://optimization.mccormick.northwestern.edu/index.php/Interior-point_method_for_LP#Barrier_Method My initial reasoning was that since the example there starts with constraints…
mavavilj
  • 7,270
0
votes
1 answer

Analytical and/or Geometrical example of a certain function

I need an example of a function that is continuous on some interval $I$, has a local minimum but doesn't have a global minimum. In other words, the problem of finding the global minimum of that function on an interval $I$ yields no solutions. Does…
Nick202
  • 149
0
votes
1 answer

For a given number n, Maximize product of numbers such that sum of these equals n

For some ${n \in \mathbb{N}}$ and ${f(x_1, x_2, x_3, x_5,...) = 1^{x_1}.2^{x_2}.3^{x_3}.5^{x_5}.7^{x_7}....}$ ${x_i \in \mathbb{W}}$ Find ${x_1, x_2, x_3, x_5,...}$ such that ${f(x_1, x_2, x_3, x_5,...)}$ is maximum and ${1.x_1 + 2.x_2 + 3.x_3 +…
Akshay Mariyanna
  • 3
  • 2
0
votes
1 answer

Standing Point Of Exponential Function Combined With Polynomial

How to Find Minimum Of the below function using Calculus Method? $$f(x)=(x-2)e^{x-2}-(x+3)^2$$ After Differentiating Once, the equation turns out to be: $$f '(x)= -2e^{x-2} + 2x.e^{x-2} - 2x -6.$$ From this step to find the minimum, we need to find…
VKJ
  • 101
  • 1
0
votes
2 answers

Saddle Point Maximization

My question is that in general, is there a case where saddle point be the global max of a function? I am solving a game theory question which the optimal solution is the saddle point. Can I conclude that the optimal solution is at the boundaries?
user3425989
  • 1
0
votes
0 answers

Optimize visits so the distance of all attendees is nearly equal

We've got 5 persons: A,B,C,D and E. Each persons has a specific distance to each other person. For example: Each year, those persons have to meet x times on one of the persons house. How am I supposed to calculate how ofter everyone has to host a…
Th1sD0t
  • 101
0
votes
0 answers

Compute the minimum or lower bound for required gates

In the problem, we have a certain number of flights that the occupation time (in minutes) of each flight in the gate is determined and considered as a parameter (i.e. flight 1 occupies the gate for 50 minutes, flight 2 occupies the gate for 60…
mahdi
  • 19
  • 3
0
votes
0 answers

Significance of encoding scheme in Genetic Algorithms

In the basic structure of a genetic algorithm, we have a population which is iteratively changed via selection, crossover, and mutation. Roughly: selection biases the procedure towards individuals with high fitness, crossover combines individuals…
Roasted Yam
  • 35
0
votes
1 answer

Fitting the biggest objects into a bin first--for near-optimization: What is this called?

I have a $5,000,000 budget. And I have a list of projects with known costs. I want to use up as much of the projects' budget as is practical--but with minimal complexity. Using database logic, I can generate an ascending running total column in the…
User1974
  • 425
0
votes
1 answer

Divide N floats into M groups so that the sum of each group is as equal as possible?

Given a list of N non-negative real numbers: t = [2.99, 7.9, 24.58, ..., 3.1415, 40.4] I want to partition the elements of $t$ into $M$ groups, $g_1$, $g_2$, ..., $g_M$, so that the sum of each group is as close as possible to $sum(t)/M$, i.e.…
Penlect
  • 73
0
votes
0 answers

Is there a variation of the bounded knapsack problem with unknown weights/values?

I've tried searching on google and other places, but can't seem to pin down anything solid. Is there any variation of the knapsack problem (or is it considered another problem entirely) where the weights/values are considered hidden until the full…
fherder
  • 11
1 2 3
…
97 98