All Questions
Tagged with convex-cone nonlinear-optimization
7 questions
1
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23
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Minimization of smooth objective with conic constraint
I am interested in deriving first-order optimality conditions for
\begin{equation}
\min_{x\in\mathbb{R}^{n}}f(x)\\
\text{s.t. }x\in\mathcal{K}
\end{equation}
where $f$ is a smooth function and $\...
- 2,105
0
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0
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31
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Can this constraint be cast as a second order cone constraint?
Can someone please explain if it possible to convert the following constraint into a second order cone programming formulation:
$xy \ge ay + b$
Here $x,y$ are non negative decision variables, $a,b$ ...
2
votes
1
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342
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Cone of feasible directions and radial cone
I am trying to prove
if $A$ is convex and $x^*\in A$, then $D(A,x^*)=cone(A-x^*)$, where $D(A,x^*)=\{ d\in \mathbb{R^n}| \exists \delta >0$ such that $x^* +td \in A, \forall t \in (0,\delta) \}$ ...
- 319
0
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1
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667
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Rewrite as second order cone constraint
Can someone please explain how to convert the following into a second order cone programming formulation:
$\{(x,y,z,w,u): x,y,z,w \geq 0, (xyzw)^{\frac{1}{2}} \geq ||u||_2^2\}$
$\{(x,y,z,w,u): x,y,...
- 329
0
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1
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120
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Sufficient condition for strict minimality in infinite-dimensional spaces
Consider the following statement:
$\textbf{Statement:} $ Let $X$ be a normed space, $S\subseteq X$ and $\bar{x}\in S.$ Let $f:X \to \Bbb R$ be locally Lipschitz and directionally differentiable at $...
- 1,950
2
votes
1
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3k
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Finding Tangent Cone of a Convex Set
Consider the problem $$\text{minimize}\,\,\, -8x_{1}+x_{2} \\ \text{subject to}\,\,\,\,\,x_{2} \leq 8, \\ (x_{1}-4)^{2} - x_{2} \leq 8 $$
By using the method of Lagrange multipliers, I found the ...
user100463
0
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24
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is this sets $A(x) $ ,$B(x)$cone?
$A(x)=\{d\in \mathbb{R^n}: \nabla f(x)*d < 0\}$
$B(x)=\{d\in \mathbb{R^n}: \forall i $ $s.t. g_i(x)=0 , \nabla g_i(x)*d < 0\}$
A,B is a set related below optimization problem
$\min f(x)$
s....
- 307