Because f ∗ is defined on the dual space, we see already the fundamental role played by the dual space in duality in convex optimization. Given an optimization problem, we don't obtain a dual problem until …

For any convex optimization problem with differentiable objective and constraint function, any points that satisfy the KKT conditions are primal and dual optimal and have zero duality gap. So, it sounded like …

Dec 29, 2022 · Conclusion In a convex optimization problem, you can always solve for the KKT conditions (FONC) to achieve a set of minimizer candidates and be sure that all of them are your …

Jun 8, 2014 · I am coming across the term: non-convex optimization problem. What exactly is this non-convex structure, and how do I know by only looking at the structure of the problem, I could tell it is …

Jan 23, 2022 · In particular, why is "Convexity" so important, such that it (historically) made us interested in classifying functions as either Convex or Non-Convex? I found Roman J. Dwilewicz's A short …

Convex Optimization is a mathematically rigorous and well-studied field. In linear programming a whole host of tractable methods give your global optimums in lightning fast times. Quadratic program...

Jul 27, 2019 · Just a new guy in optimization. Is it true that all convex optimization problems can be solved in polynomial time using interior-point algorithms?

Apr 9, 2020 · This is the convex problem where the dual problem has no feasible solution and KKT conditions have no solution but the primal problem is simple to solve. $ {\bf counter-example 5}$ For …

I also like of course Rockafellar's old but still fantastic Convex Analysis, Rockafellar and Wets' Variational Analysis. For teaching/selfstudy, Mordukhovich and Nam's An easy path to convex …

Apr 10, 2020 · 8 I am looking for optimization books. Can you suggest some good materials? First, I started with Convex Optimization by Stephen Boyd & Lieven Vandenberghe, but I don't like it …