All Questions
9 questions
0
votes
1
answer
296
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Solve Linear Least Squares with $ {L}_{1} $ Norm Regularization with Linear Equality and Non Negativity Constraints
I'm searching for a way to solve the following problem in MATLAB.
$$\begin{array}{ll} \text{minimize} & \|Ax-b\|_2 + \lambda \|Cx\|_1\\ \text{subject to} & D x = 0\\ & -x \leq 0\end{array}$...
2
votes
1
answer
558
views
Simple implementation of interior point method
I am trying to build a simple implementation of the interior point optimization method using MATLAB. I am looking forward to solving a very simple system (2 variable) of constrained quadratic ...
1
vote
0
answers
88
views
Nonlinear optimization of a matrix with the costraint to be orthonormal
I'm trying to find the matrix x which minimize the following cost function :
$J =||B_b -x*B_n||^2$
with the constraint that x has to be an orthonormal matrix.
I'm trying to use MATLAB fmincon tool, ...
1
vote
0
answers
88
views
Schatten-1 norm as matrix constraint
suppose I have a tensor $x \in \mathbb{R}^{n \times 2 \times 3}$. I take the seminorm of $x$ given by taking the Schatten-1 Norm in every $2 \times 3$ slice and then the $\ell_1$-Norm of the resulting ...
- 349
1
vote
0
answers
412
views
Difficulty implementing logarithmic barrier in Matlab.
I'm trying to create a convex optimization code in Matlab , to deal with inequality constraints I'm using logarithmic barrier.Suppose we have inequality $g(x) =< 0$ to satisfy,so I define $\varphi ...
- 403
-1
votes
1
answer
840
views
Solve Convex Optimization Using MATLAB's `fmincon()` Function
Is it guaranteed that "fmincon" in MATLAB can uniquely find the minimizer of a convex optimization problem? As I see, it heavily depends on the initial point and finds just a local min (if it can).
...
- 15
2
votes
0
answers
838
views
Writing an accurate SDP solver in Matlab
As part of a research project I'm supposed to write an semidefinite programming solver in Matlab (similar to SDTP3, MOSEK, SEDUM, etc) except it needs to be able to solve to many significant digits ...
- 121
3
votes
3
answers
4k
views
How to Project onto the Unit Simplex as Intersection of Two Sets (Optimizing a Convex Function)?
I would like to estimate a matrix $S$ by solving the following optimization problem
\begin{align}
&\min\limits_{s} f(S) \\
&\text{subject to }\sum_{i,j}s_{i,j}=1,\quad s_{i,j}\geq0~\forall(i,...
- 771
1
vote
1
answer
234
views
Free software or algorithm for Second-Order Cone Program
I need to solve the following optimization problem:
$$
\mathbf{x}^\ast = \operatorname{argmin}_{\mathbf{x}} \Vert \mathbf{Rx} \Vert_2^2 \;\;\; \mathrm{s.t.} \;\;\; \mathbf{s}^\mathrm{H} \mathbf{x} = ...
- 3,565