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.

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The requirement of compactness for the Strict Separation Theorem

In class I learned about the following theorem: Strict Separation Theorem: Let $A$ and $B$ be two closed convex subsets of $\mathbb{R}^n$ with that $A \cap B = \emptyset$. Furthermore assume that $A$ ...
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Is it possible to compute $-\log\left({\sqrt{1.8\times 10^{-5}\times 0.1}}\right)$ without a calculator?

The following question is part of a chemistry problem that came in the Dhaka University admission exam 2013-14. What is $-\log\left({\sqrt{1.8\times 10^{-5}\times 0.1}}\right)$? (a) 2.672 (b) 2....
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How is the Wilson-Han-Powell SQP algorithm applied?

Say for example we need to minimize $x_2$ subject to $x_1^2+x_2^2-1=0$ starting at $x_1=x_2=1/2$ and using $B=\nabla^2[x_2+\lambda(x_1^2+x_2^2-1)]$ with $\lambda=1$. Now, the WHP-SQP algorithm goes ...
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how can I linearize a constraint of the form sum(min(x(i),y(i))) for a linear optimisation problem?

I have an linear optimisation problem and I'd like to impose a constraint of the following form: $∑_{i=0}^N min⁡(x_i,y_i)≥C$ where x_i,y_i are rational numbers greater or equal to 0. how can I ...
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Find Matrix A such that $\operatorname*{argmin}_A ||H-A||^2_F + |A|_1$ from given matrix H [closed]

Question I have matrix H, I want to find Matrix A such that: $$\operatorname*{argmin}_A ||H-A||^2_F + |A|_1$$ How can I do that? What's the updating rule for A? Can someone please guide?
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What does it mean that a function is unbounded below in every neighborhood?

In this paper Strong Convexity Does Not Imply Radial Unboundedness In [3], Tapia gives this result showing that a strongly convex functional is either radially unbounded (and so minima-existence ...
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Ensure continuity on the first-order derivative while minimizing functional

Consider the problem of minimizing a functional $F[x,u(x),u'(x)]$ subjected to $N$ constraints of the type $g_i(x,u,u')=0$ at different positions $x=x_i$, such that the first-order optimality criteria ...
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Find the point on the plane $x+2y+3z=13$ that is closest to the point $(1,1,1)$ [closed]

Recently, I received the following task. I would be very grateful for your help. Find the point on the plane $x+2y+3z=13$ that is closest to the point $(1,1,1)$. How would you minimize the function?