Tagged Questions

Convex Optimization is a special case of mathematical optimization. It includes Linear Programming and least-squares.

45 views

Least squares with multiple linear constraints

The method of direct elimination can be used to solve the constrained least squares problem $$\min_{\mathbf{x}}\left\Vert \mathbf{Ax}-\mathbf{b}\right\Vert _{2}$$ \begin{...
20 views

Can the low-rank approximation problem be formulated as the following convex model?

Given a three-order tensor $\mathcal{Y}$, our aim is to find a tensor $\mathcal{X}$ to approximate it and $\mathcal{X}$ should satisfy the following property: $\mathcal{X}$ can be well approximated ...
39 views

Quasiconvexity of a function on the positive orthant using rays

It is seen in Boyd's book on Convex Optimization book that to show a function $f:\mathbf{R}^n\rightarrow \mathbf{R}$ is quasiconvex, it is enough to show that $f$'s restriction to a line is ...
44 views

Proving equivalent optimization problems

Consider the problems $\min f(x) , x \in X$ and $\min g(x), x \in X$. two optimization problems are said to be equivalent if an optimal solution to one, is also optimal to another. I would like to ...
47 views

Is the constraint $xy\leqslant 0.001$ convex?

I would like to ask whether the constraint $xy\leqslant 0.001$ ($x,y\geqslant0$) is convex. Since its Hessian matrix is positive semi-definite for $x,y\geqslant0$, the constraint $xy\leqslant 0.001$ (...
28 views

Convexity of n $4u^4x^{2.5}y^{-5}$ over $x>0, y >0$ and $u>0$

I am trying to find if the function $4u^4x^{2.5}y^{-5}$ is convex over $u>0, y>0$ and $x>0$. The thing which comes to my mind immediately is to check the positive semi-definiteness of the ...
So for the dual part of the complementary slackness, the theorem says this: If $y_i^* > 0$, then the $i^{th}$ constraint is binding in Primal $\ \ \ (1)$ If the $i^{th}$ constraint in Primal is ...