Tagged Questions

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.

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Inverse Vectorization Vec^-1

Hope that you will find this post in good health. I am Mr. Adnan from Pakistan with research background in Control systems. I am working on one problem in which Hadamard weights are using. During ...
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Maximizing area of a pentagon

Suppose $a,b,c,d,e$ are pairwise distinct positive integers. Consider a pentagon with sides $a,b,c,d,e$ and with angles maximizing its area (we assume that a pentagon with such sides exists). It is ...
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Individually checking constraints for convexity in Optimisation problem valid?

I have a quadratic minimisation problem where both the objective fn and constraints have some quadratic terms. (Such as a throttle variable (continous) * On/Off (integer variable)). My question is: ...
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Minimization of vector sum through rotation

I'm curious if there's an algorithmic way to find the minimal vector sum of $N$ vector magnitudes by applying a rotation $\Phi$ to each individual vector. As an example in two dimensions, if I have ...
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Find pressure in a sinusoidal function

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with laughing gas. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 ...
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Optimized placing of same-size squares into rectangles

Suppose that we have several squares of the same size. We want to draw n rectangles (red and yellow rectangles here) to contain these squares. The goal is to have ...
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Is it possible to convert a loss function minimization problem into an eigenvector problem?

I have a very vague feeling that the problem of optimizing a loss function is related to the problem of finding the smallest/biggest eigenvector. However, I don't have the expertise to see this ...
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Cutting a pie into 2 unequal peices with a single cut, minimising its length. [closed]

Suppose we have a circle with an area of 1, which we are to cut into two pieces, of area (x) and (1-x) respectively. Let x<0.5. How should we make the cut, to minimise its length? What is the ...
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Solving Equations involving max operation

I would like to know how to solve this set of equations for v*(h) and also v*(l) Assume all other variables are known..concentrate on the 3rd equality in case of v*(h)..the first 2 are not needed. I ...
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Algorithm for scheduling event observers

I'm reviewing different algorithms to solve a scheduling problem and was hoping someone with a better breath in the area might help me focus on the right class of algorithms. Basically the problem is ...
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Maximum of Contour Line

Consider the potential $U(x,y)=ay^{2}+b(e^{x-y}-1)^{2}+c(e^{x+y}-1)^{2}$ where $a$, $b$ and $c$ are known constants. I want to move through a contour line of this potential $U(x,y)=k$, say $y=g(x)$. ...
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Expressing an inequality constraint as a linear matrix inequality (LMI)

I am trying to formulate an optimization problem as a semidefinite program (SDP). My optimization variable is $\bf x = [x_1,\dots,x_N]'$, where $\bf x$ is an $N \times 1$ vector, and one of my ...