All Questions
564 questions with no upvoted or accepted answers
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Computing maximum point for minimal function of a family of linear functions
Let $x \in S^n $ where $S^n = ${$ [x_1,x_2,...,x_{n+1}]\in \mathbb{R}^{n+1} \mid x \ge 0 , \sum x_i = 1 $} and let $f_i : I^n \to \mathbb{R}$ be a finite $m$-sized family of LINEAR functions such that:...
- 11
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783
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LP relaxation for ILP\IP (integer linear programming)
I am familiar with LP relaxation for ILP (or IP). Assume we concern with integer minimization problem, which we formalize using ILP; we then relax the ILP into LP and we say that the LP provides a ...
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191
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Differentiability of minimax objective function with respect to a decision variable
I have the following optimization problem:
$$\text{find } x= \min_{a} \max_{\lambda\in\Lambda} |R(h\lambda)|$$
where $\Lambda$ is some finite, fixed set of complex numbers and $R(z)$ is a ...
- 1,253
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1k
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A question regarding Danskin's theorem
Suppose $\phi({\bf x},{\bf z})$ is a continuous function of two arguments,
$\phi: {\mathbb R}^N \times Z \rightarrow {\mathbb R}$,
where $Z \subset {\mathbb R}^m$ is a (non-empty) compact convex ...
- 13
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237
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Conic fitting with pseudoinverse technique
I am trying to fit points of an ellipse to my model using pseudoinverse technique described in this paper (it's in section 4.1). I'm sure that my understanding is wrong, please, could you give me ...
- 101
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118
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sparsest cut always has solution
Hi!
How to prove that sparsest cut always has an optimal solution which is the cut for some vertex-subset.
Looks like it's should be a kind of fundamental theorem for sparsest cut. But I didn't ...
- 1
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271
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L1-regularized Least Squares on a matrix with Toeplitz Blocks (not block-Toeplitz)
I am trying to speed up a sparse signal recovery algorithms.
My sensing matrix is a set of Toeplitz Blocks, M = [T1,T2,T3,...,Tk]
The objective is min ||Mx - b||_2^2 + ||x||1
What I'm actually ...
- 2,383
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727
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Decomposing max-convolution of sum of functions ?
Hello.
$R, F_1, F_2, F_3$ are random (not-convex, not-concave) 2D matrices of size 100x100.
$R$ is a linear combination of $F_1, F_2, F_3$.
Explicitly, $R = w_1 F_1 + w_2 F_2 + w_3 F_3$
where $w_1,...
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825
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Combining Convex and Concave in CVX
Hello,
I have an unconstrained optimization in which I need to minimize a sum of convex functions and maximize a concave function together. I combined both the problem by adding a minus sign to the ...
- 121
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215
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interdependence of decision variables
Dear all,
its quite clearly stated that independence of decision variables are necessary for solving optimization problems using the simplex method.
Is this a requirement for all linear ...
- 1
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1
answer
153
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Difference of two optimization problem's optimal value
Let we have two following optimization problems:
\begin{align}
\text{(P1)}\quad \alpha_1 = \max_{x_1,\ldots,x_M} &\quad \sum_{m=1}^{M}\log(1+f_m(x_1,\ldots,x_M))\\
\textrm{s.t.} &\quad \...
- 287
0
votes
1
answer
180
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(probably simple) optimization question
Suppose you have a concave function defined over a non-polyhedral convex cone and you are interested in the infimum. What would be standard approaches to tackle the question? (The cone is actually PSD ...
- 6,962
-1
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1
answer
267
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To what equal constant in the Gibbs lemma
The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is:
Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...
- 1,329
-2
votes
1
answer
332
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A kind of economic objective function in assignment
I recently thought about a concept that seems like it should come up in economics, but I don't know if there's a name for it and where people would have encountered it elsewhere: Suppose we have a ...
