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 problem. …

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 …

Nov 2, 2016 · However, $-xy$ is neither convex nor concave. According to Boyd's book on convex optimization, the definition of a convex optimization (Equation (1.8) in the book) requires that the …

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 …

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 …

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 …

Jan 12, 2013 · Other books I recommend looking at: Introductory Lectures on Convex Optimization: A Basic Course by Nesterov, Convex Analysis and Nonlinear Optimization by Borwein and Lewis, …

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 …