# What is Optimization: Definition and 627 Discussions

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.

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1. ### A Are these two optimization problems equivalent?

Hello, I need help please. I have the following optimization problem defined as \begin{aligned} & (\mathbf{P1}) \quad \max_{\mathbf{z}} \quad \left| d -\sum_{n=1}^{N} \frac{c_n}{f_n + z_n} \right|^2 \\ & \text{subject to} \quad \sum_{n=1}^{N} \frac{|a_n|^2 \text{Re}(z_n)}{|f_n...
2. ### A Parameter optimization for the eignevalues of a matrix

Hello! I have a matrix (about 20 x 20), which corresponds to a given Hamiltonian. I would like to write an optimization code that matches the eigenvalues of this matrix to some experimentally measured energies. I wanted to use gradient descent, but that seems to not work in a straightforward...
3. ### A How can I group this data?

I have a matrix of dimension 56*56, each row and column represent the compatibility of one person with the rest of the people. A sample matrix could be Alejandro Ana Beatriz Jose Juan Luz Maria Ruben...
4. ### I Optimization problem with multiple outputs: impossible?

Hello, I'm facing a practical optimization problem for which I don't know whether a standard approach exists or not. I would have liked to rephrase the problem in a more general way, for the sake of "good math", but I'm afraid I would leave out some details that might be relevant. So, I'm going...
5. ### Optimization of barrel length in pneumatic cannons

I was checking bait cannons and potato guns on the internet because they are fun. Maybe one day I'll build my own. First of all, these cannons use multiple sources of energy (combustion using hair spray, dry ice, etc.). I'll just consider compressed air cannons because I think they are the most...

36. ### Optimization problem - right circular cylinder inscribed in cone

Please I do not want the answer, I just want understanding as to why my logic is faulty. Included as an attachment is how I picture the problem. My logic: Take the volume of the cone, subtract it by the volume of the cylinder. Take the derivative. from here I can find the point that the cone...
37. ### I Frechet Derivatives & Optimization - Mechanics Example

Allegedly Frechet derivatives are used in optimization problems in mechanics, but I have not found a clear example of this. Does anyone know of an example to go through? I would think because of the significance of Lagrangian mechanics that it could be more related to a variational calculus...
38. ### MHB How to solve following optimization problem?

The following is the mathematical expression for my model's rate expression. Variables $x,y$ are the controlling parameter, while the rest are positive constants. $$\max_{x,y} \ ax + by^3 \ (s.t. \ 0\leq x \leq 1,\ 0\leq y\leq1)$$ Can I mathematically say that it is a convex problem within...
39. ### Fortran GFORTRAN Optimization Question

I am trying to troubleshoot why GFORTRAN versions beyond 5.4 will not compile with optimization on some of my .f source. You can request options included in each level by: Gfortran -Q -O1 --help=optimizers > listO1.txt (as an example) When I enter the enabled flags individually and compile...
40. ### I Multivariable optimization problem

Hi all, (Please move to general or mechanical engineering sub-forum if more appropriate over there. I put this here as it is essentially a mathematics problem.) Broken into sections: - problem categorization (what type of problem I think I have), - the question, - specifics (description of the...
41. ### MHB Max & Min Values of $S$ for $x_1^2 + x_2^2 = y_1^2 + y_2^2 = 2013$

Find the maximum and the minimum values of $S = (1 - x_1)(1 -y_1) + (1 - x_2)(1 - y_2)$ for real numbers $x_1, x_2, y_1,y_2$ with $x_1^2 + x_2^2 = y_1^2 + y_2^2 = 2013$.
42. ### Java JavaFX layout not updating and email sending optimization problem

I am writing a java application that would let me bulk send emails. The first problem I have is that of performance; approximately 15 seconds per 5 emails. The second problem, which is the more important, is that my JavaFX is not updating the scene. My code below shows that the way I intended...
43. ### A Differential Equations (Control Optimization Problem)

$$y_{1}{}'=y_1{}+y_{2}$$ $$y_{2}{}'=y_2{}+u$$ build a control $$u \epsilon L^{2} (0,1)$$ for the care of the appropriate system solution $$y_{1}(0)=y_{2}(0)=0$$ satisfy...
44. ### Optimization of the distance from the point on an ellipse

My Attempt :We need to maximize ## D=\sqrt{x^2+(y+2)^2} ## subject to the constraint ##4x^2 + 5y^2 = 20##. From the constraint equation, we can write ##x^2=\frac{20-5y^2}{4}## Using this in the formula for distance, ##D=\sqrt{\frac{20-5y^2}{4}+(y+2)^2}## Differentiating this wrt y, and...
45. ### Linear optimization problem

attached resolution attempt
46. ### I Optimization of multiple integrals

The Euler Lagrange equation finds functions ##x_i(t)## which optimizes the definite integral ##\int L(x_i(t),\dot x_i(t))dt## Is there any extensions of this to multiple integrals? How do we optimize ##\int \int \int L(x(t,u,v),\dot x(t,u,v))dtdudv## ? In particular I was curious to try to...
47. ### I QM through stochastic optimization on spacetimes

I have a simple question as a layman in the field: Is this worth reading, and even more, is it a contribution to possibly shorten the endless discussions in this subforum? https://www.nature.com/articles/s41598-019-56357-3.pdf
48. ### Quantum computing & chill

A thing doing its own thingy thing could compute faster than a computer can compute.
49. ### MHB Optimization calculus question (Difficult)

A truck crossing the prairies at constant speed of 110km per hour gets 8km per litre of gas. Gas costs 0.68 dollars per litre. The truck loses 0.10 km per litre in fuel efficiency for each km per hour increase in speed. Drivers are paid 35 dollars per hour in wages benefits. Fixed costs for...
50. ### Optimization problem (Max area of a combined semi circle and a square)

A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l. Find the maximum area when the combined perimiter is 8 meter. I first try to construct the a function for the perimeter. 2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7 Next I insert this...