Resources on Solving Convex Optimization Problems in the Compressed Sensing Field

1. How can we solve a convex optimization problem?
2. How do you prove an optimization problem is convex?
3. Do convex optimization problems have a unique solution?

How can we solve a convex optimization problem?

Convex optimization problems can also be solved by the following contemporary methods: Bundle methods (Wolfe, Lemaréchal, Kiwiel), and. Subgradient projection methods (Polyak), Interior-point methods, which make use of self-concordant barrier functions and self-regular barrier functions.

How do you prove an optimization problem is convex?

Algebraically, f is convex if, for any x and y, and any t between 0 and 1, f( tx + (1-t)y ) <= t f(x) + (1-t) f(y). A function is concave if -f is convex -- i.e. if the chord from x to y lies on or below the graph of f.

Do convex optimization problems have a unique solution?

In fact a convex optimization problem may have 0, 1 or uncountably infinite solutions.