# Tagged Questions

Mathematical and computational method for finding the best outcome in a given mathematical model where the list of requirements is represented as linear relationships.

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### Brute Force Search Algorithm for Semidefinite Programming (Representation of Spectrahedron)

I was wondering if there exists a brute force search algorithm for semidefinite programming problems. Specifically, can we find finite number of points in the positive semidefinite cone such that for ...
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### List of Pivot rules for simplex methods

Any implementation of the simplex method depends on the choice of pivot rule, which determines how the corners of the search space polyhedron are traversed. Many different have been proposed ...
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### Vector Product in the constrinats on an optimization problem

Can the following optimization problem be solved using Semi-Definite Programming or Linear Programming. We are given a data matrix $A$, which is known. We have the following optimization problem. This ...
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### Are there integer programs with small coefficients that only have large solutions?

It is well-known that if an integer linear program has a feasible solution, then it has a feasible solution whose bit size is polynomially bounded. For example, here is Theorem 13.4 from Papadimitriou ...
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### Linear programming with superpolynomially many constraints?

(The specific problem I have is stated as precisely as I could in the very last paragraph which starts with a boldface "Question:", up until then the question provides context for it.) Say we have an ...
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### Inclusion of polytopes

Consider the following two system of linear (in)eqaulities: $S = Ax \leq b;\; Cx = e$ $T = Dx \leq d;\; Gx = g$ How can I check if $S\cap \neg T=\emptyset$ where $\neg T$ is the complement of the ...
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### Equivalence of weighted Minkowski sums

Given $n$ polytopes $P_1, \cdots, P_n$, each $P_i$ is given as the V-representation, i.e., a set of $m$ points as its set of vertices. Furthermore, consider a variant of the Minkowski sum (somehow ...