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Tagged Questions

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0answers
16 views

minimize a cost function with matrix traces

Hi, I have a cost function of the form F(X) = tr{X'AX}+tr{X'B} , s.t. X'X=I X is a m by n, m>n matrix with orthonormal columns. A is symmetric m by m, not necessary positive defi …
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0answers
129 views

Tools for “infinite-dimensional linear programming”

I was wondering, whether you could point me to some tools with which I could tackle the following "infinite-dimensional linear programming" problem: Notation: $a=1,2,\ldots, A$, …
3
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1answer
120 views

Delta-convex functions and inner products

A delta-convex (d.c.) function is one which can be written as the difference of two convex functions. The space of d.c. functions includes all C2 functions, and is interesting bec …
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57 views

How to prove equivalence of two Semidefinite optimization models?

I want to prove that the following two models are equivalence. Is there any suggestion that how could be proved? First model: $$\min ~~ E | y| $$ $$~~~~~~~~~~~~s.t. ~~\langle I, …
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1answer
84 views

solve non-convex quadratic constrained quadratic programming

$\min_{\beta}\beta^{T} A \beta$ $s.t. \ \beta^{T} C \beta=1\ and\ \beta\geqslant 0$ Here $A,C\in \mathbb{R}^{M\times M}$, $\beta \in \mathbb{R}^{M}$ I saw in one paper saying t …
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2answers
159 views

On a version of gradient descent

I am trying to read this paper and have gotten stuck. The author considers the problem of minimizing a convex function whose gradient has Lipschitz constant $M$ and considers the s …
2
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0answers
94 views

Incremental minimum spanning tree

Given a connected graph $G=(V,E)$ with a weight function $w:E\to\mathbb{R}$ and a subset $E_0\subseteq E$ such that the subgraph $(V,E_0)$ is connected, I am looking for a sequence …
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100 views

A detail in the proof of the Motzkin-Straus theorem

The Motzkin-Straus theorem says that the global optimum of the quadratic program $$\max f(x)=\frac{1}{2} x^{t}Ax,\qquad \mbox{ subject to }\sum x_{i}=1 \mbox{ and } x_{i}\geq 0,$$ …
2
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1answer
56 views

How to maximize the determinant of a matrix of the form VDV^H

Hi, I have a matrix of the form $A=VDV^H$, where $V$ is a $M \times 2M$ complex matrix, $D$ is a $2M \times 2M$ diagonal real matrix, thus the dimension of $A$ is $M \times M$. …
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0answers
65 views

A tricky optimization problem over matrices

Hi I have the following problem whose solution has lured me for some months now.... All matrices are complex $N\times N$. Let $A$ be a positive definite matrix with all eigenvalue …
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0answers
31 views

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_ …
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0answers
75 views

null controllability of linear wave equation

Consider the linear wave equation : $$z_{tt}=\Delta z + k(x) z + h(t) , \; in \; \Omega\times (0,T)$$ Are there sufficient conditions on the functions $k(x)$ and $h(t)$ for which …
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0answers
88 views

Quadratic optimization with parameter in constraint

Disclaimer: I posted the same question on math.stackexchange. However, the FAQ suggests to post research-level questions in this forum. Question: Given a function $q: \mathbb R^{N …
1
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0answers
61 views

A Conjecture related to minimization of product of determinants over permutations

Hi I have the following problem (and a conjecture which holds in Matlab). Given an $N\times N$ matrix $H$, represent it by its $2N\times 2N$ real-valued representation (which I wi …
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29 views

Vehicle Routing Problem with several constraints.

I need to consider the vehicle routing problem(VRP) with following constraints: 1) The number of vehicle is $N$. 2) The number of deport is $M$. 3) Different vehicles have diffe …

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