Questions tagged [global-optimality]
Use this tag for questions relating to an optimal (best) solution which attains the best objective function value over the entire set of feasible solutions.
6
questions
8
votes
1answer
79 views
Problem solvable $\Rightarrow$ subproblems solvable if feasible region closed, convex?
Let $c \in \mathbb{R}^n$, $M \subseteq \mathbb{R}^n$ such that the problem
\begin{align}P:\quad\min_{x \in \mathbb{R}^n}&\quad c^\intercal x\\\textrm{s.t.}&\quad x \in M\end{align} is solvable....
11
votes
1answer
382 views
Solvers and saddle points
It seems like most solvers that can tackle nonlinear nonconvex optimization problems (e.g. IPOPT) operate on ultimately solving for the first-order optimality conditions. Can it therefore be assumed ...
11
votes
1answer
168 views
Recovering primal optimal solutions from dual sub gradient ascent using ergodic primal sequences
My question concerns recovering a primal optimal solution while performing dual sub gradient ascent. Denoting by $y_i$ the dual multiplier in the $i^{\text{th}}$ iteration, let
\begin{equation}
x_i = ...
22
votes
4answers
1k views
What is a solution?
Consider a standard optimization problem: Minimize an objective function with respect to constraints. My question is:
What does the term "solution of the optimization problem" mean?
At first I ...
10
votes
1answer
104 views
Termination Criteria of Solver in Pyomo
I am solving a nonlinear optimization problem using Pyomo with Ipopt as solver. The solver exits with the status:
EXIT: Optimal Solution Found.
This I can cross ...
14
votes
4answers
334 views
CPLEX non-convex Quadratic Programming algorithms
CPLEX solves non-convex quadratic problems to global optimality with a global optimality option (in version 12). The relevant pages are
this and this. I benchmarked many solvers, and see that CPLEX ...
