# Questions tagged [duality-theorems]

For question about the concept of dual, either in the sense of vector spaces, topological group or dual problems.

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### Dual isogeny of purely inseparable isogeny is not always purely inseparable

Let $φ$ be purely inseparable isogeny of elliptic curves. Then, dual isogeny of $φ$ is always purely inseparable? Background Super singular elliptic curve over a field of characteristic $p$ is defined ...
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### What is the infimum over $x$ of the lagrangian function?

I am learning about duality in convex optimisation. The Lagrangian is defined as $$L(x, \lambda, \nu) = f_0(x) + \sum_{i=1}^m\lambda_if_i(x) + \sum_{i=1}^p\nu_ih_i(x)$$ where suppose the optimisation ...
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### Finding Co-Differential from Differential in Homology

I am trying to use Algebra; Linear and otherwise to find the co-differential ,i.e., the differential operator d in a Cohomology Theory starting with homology. For now, I just wanted to start with a ...
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### Linear programming duality theory general question [closed]

Does duality theory imply that if the primal problem is infeasible, then its dual is either infeasible or unbounded? How would this be proven?
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### General primal and dual solutions

We are given primal $$\text{max: } z = c_1x_1 + c_2x_2 + ....c_nx_n \\ \text{subject to: } a_1x_1 + a_2x_2 + .... a_nx_n \leq b \\ x_1, x_2, ...,x_n \geq 0$$ And we have to find the dual and then ...
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### Konig's Matrix Proof by Dilworth's Thm [duplicate]

Let M be a (0, 1) matrix; that is, a matrix where each of whose entries is either a 0 or a 1. A line in M is either a row or a column of M. Use Dilworth's theroem to prove that the minimum number of ...
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