The process of determining the best solution among all possible solutions given a set of constraints.

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Good algorithm for in-experiment 1-D optimization?

I'm running an experiment -- for the question, it doesn't matter which one, but I'm measuring an optical intensity $I$ as a function of two parameters: reflection angle $\theta$ and wavelength ...
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Coefficients and Parameters for contracted Gaussian basis sets

This is a repost from Chemistry.stackexchange in the hopes that someone here will be able to help me. Any help at all would be greatly appreciated. As far as I understand, an STO-NG contracted ...
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67 views

Particle Collision with Static System

I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is : The method by which I can reduce the number of ...
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Optimal Airplane trajectory

The last time I took a plane the following problem crossed my mind. Setting: take the Earth and neglect its rotation around the Sun. It then only rotates on itself with angular velocity $\Omega$. ...
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Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
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86 views

Pareto efficiency and Standard Model parameters

Pareto Efficiency is a well understood concept in economics, which basically is a condition where no one actor could be made better off without some one being made worse off. This condition allows ...
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Dual methods in structure optimization

I am studying Structure Optimization, and the teacher took a few weeks to detail dual methods, but I don't get why it is useful. From an optimization problem with ...
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37 views

Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
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Optimization of a functional defined implicitly

I would like to minimize a functional of the type: $$L[\gamma]=\int_a^b F(T(\gamma(t))dt$$ on the space of paths $\gamma$, where $T=T(\gamma,t)$. Now, usually I would simply apply Euler-Lagrange's ...
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range of the difference of two-qubit density matrix determinants

The determinant of a two-qubit (4 x 4) density matrix lies between 0 and (1/2)^8. (A pure state has determinant zero, and the fully mixed [classical] state, determinant (1/2)^8.) The determinant of ...