Tagged Questions
0
votes
1answer
31 views
How to re-parametrize for quadratic minimization?
Given a real-rectangular matrix $S$ and inorder to solve this simple quadratic programming problem:
Minimize $w'S'Sw = \|S w\|^2$ over $w$ subject to
$e^Tw = 1$ and $w \geq 0$
using a solver I ...
0
votes
1answer
52 views
Infeasible start Newton's method
I am implementing infeasible start Newton's method from the information in the slides (slide 11 of the link) posted here. It requires us to calculate primal and dual Newton steps, denoted by, $\Delta ...
2
votes
0answers
143 views
Optimization problem about large matrices
I'd like to solve the following optimization problem:
Find non-negative scalar $a$, $b$, $c$ to minimize
$\| (D-(aA+bB+cC+D^{-1})^{-1})y\|^2+2\operatorname{trace}((aA+bB+cC+D^{-1})^{-1})$
where ...
0
votes
0answers
22 views
How can I reformulate my problem to make it convex?
I would like to find the symmetric positive definite matrix $S\in \mathcal{M}_{m,m}$ that minimizes the function $f(S)=\mathrm{trace}(S)+m^2\mathrm{trace}(S^{-2})$ which has been proven to be convex ...
1
vote
0answers
16 views
Can we express a SPD matrix $S$ in terms of $S^{2}$ in a different manner to solve a convex problem?
I have to find the Symmetric Positive Definite matrix $S\in \mathcal{M}_{m,m}$ that minimizes the function $f(S)=\mathrm{trace}(S)+\mathrm{trace}(S^{-2})$ which has been proven to be convex in the ...
0
votes
0answers
110 views
Gradient Descent with nonlinear constraint on Symmetric positive definite matrix space
I would like to find the stationary point $S_*$ (global minimum) that minimizes the function $f(S)=\mathrm{trace}(S)+m^2\mathrm{trace}(S^{-2})$ which has been proven to be convex in Convexity of ...
2
votes
1answer
50 views
Possibility of Unboundedness in Least Squares Minimization
Suppose we have the quadratic minimization problem
\begin{equation}
\min_x \frac{1}{2} x^TPx + q^Tx +r
\end{equation}
We know that when $P$ is symmetric positive semi-definite, but the optimality ...
0
votes
1answer
122 views
What Stopping Criteria to Use in Projected Gradient Descent
Suppose we want to solve a convex constrained minimization problem. We want to use projected gradient descent. If there was no constraint the stopping condition for a gradient descent algorithm would ...
0
votes
1answer
136 views
Numerical optimization with nonlinear equality constraints
A problem that often comes up is minimizing a function $f(x_1,\ldots,x_n)$ under a constraint $g(x_1\ldots,x_n)=0$. In general this problem is very hard. When $f$ is convex and $g$ is affine, there ...
1
vote
1answer
335 views
what are Smooth and Non Smooth Problem in optimization?
I am trying to understand the difference between the optimization problem types which are basically smooth and non smooth. I also found this question what does a smooth curve mean? I understand that ...
4
votes
1answer
281 views
Solving a set of 3 nonlinear equations with constraints
Problem statement:
I am given 3 sets of equations that govern the force $P$, and also the neutral axis, defined by two variables, the radius from the center $r$ and also the rotation degree in ...
