# Tagged Questions

28 views

### L1 regularized SVM in Matlab

Minimizing the following SVM formulation \begin{align} \arg\min_{\mathbf{w}}\frac{1}{2}\|\mathbf{w}\|^2_2 \\ \text{subject to } \quad y_i(\mathbf{w}\cdot\mathbf{x_i}) \ge 1 \end{align} can be done ...
26 views

### Reference for gradient descent with unit norm constraint

I faced a non-convex optimization problem with unit norm constraint. I can solve the problem using the gradient descent method and the projection of the gradient onto the tangent plane as in @joriki ...
28 views

### multi-objective optimization

I am currently encounterring a optimization problem. The goal is optimize an objective function A and B at the same time. But the problem is that optmizing A will almost always tradoff with B, such ...
35 views

### Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
89 views

### What numerical methods are known to solve $L_1$ regularized quadratic programming problems?

What numerical methods are suitable to solve the following problem $$\min_x \tfrac{1}{2}x^T A x + b^Tx + \lambda ||x||_1$$ where $x,b\in\mathbf{R}^n$, and $A\in \mathbf{R}^{n\times n}$ is positive ...
34 views

### Strong convexity of a function with cases

Given a set $S = \{x_1,\dotsc,x_n\} \subset \mathbb{R}$, is the function \begin{align} f&: (0,\infty) \to \mathbb{R} \\ f&(p) = 2p^2 + \frac{1}{n}\sum_{i=1}^n \max(0, -p^2-x_i) \end{align} ...
23 views

### dual value of a linear constraint

Assume a minimization problem. The dual of an inequality '<' constraint is the marginal improvement in the objective function (ie marginal reduction) by marginally increasing the right-hand-side ...
50 views

24 views

27 views

74 views

### Can $\min f'x$ s.t. $(a'x - b)^2 \le d$ be written as a SOCP?
It does not appear to be significantly different from the form listed here: http://en.wikipedia.org/wiki/Second-order_cone_programming with (in article notation) $i = {1}$, $A = a$, and $b$, $d$ as ...