In the case of a convex optimization problem, is there any obvious reason to expect that strong duality should (usually) hold? It often happens that the dual of the dual problem is the primal …

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 …

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. …

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 …

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. …

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?

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 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 …

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 …

The general point of convex problems is that a local minimum is a global minimum. There are all sorts of relaxations and generalizations (or transformations as in posynomials), but generally …