# Questions tagged [convex]

A convex set includes all points lying between any two points from the set. A convex function on such a set is a function lying below any straight line connecting two points from its graph. Convex optimization is concerned with searching for the minimum of such a function.

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### If we add a constant weight vector with an absolute function, does it still remain convex then?

We know that absolute functions are convex. Now what if we add a constant weight vector to it, does it still remain convex? Say the equation is Absolute loss regression + L1 regularization, we know ...
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### Is there a smart algorithm of finding the maximum of $X^{\top}a$ with $X$ and $a$ both belong to some compact convex set? [closed]

Suppose $X\in\mathcal{X}\subset R^k$ and $a\in\mathcal{A}\subset R^k$, where $\mathcal{X}$ and $\mathcal{A}$ are both compact convex set. Is there a systematic way of finding the maximum of $X^{\top}a$...
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### Optimization textbooks for statistics and data analytics

Any statistical analysis, machine learning or data science involves some sort of optimization at the end of the day. I'm looking for good linear and nonlinear optimization textbooks for self ...
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### For convex problems, does gradient in Stochastic Gradient Descent (SGD) always point at the global extreme value?

Given a convex cost function, using SGD for optimization, we will have a gradient (vector) at a certain point during the optimization process. My question is, given the point on the convex, does the ...
My question has to do with the VC dimension of the class of convex polygons with $m$ vertices. A solution to this problem is given in the following: Advanced Algorithms. Call the class of all ...