# 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.

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### 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 ...
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### 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 ...
219 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 x_i = ...
458 views

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 ...
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### 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 ...
90 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....
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### How to determine different gap rates?

I found in the literature different gaps: a gap between a random solution and an exact solution a gap between the exact solution and a lower bound a gap between the exact solution and a lower bound a ...
174 views

### What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?

Case 1: NLP When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However,...
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### Does Dijkstra's algorithm find the optimal solution for a weighted and directed shortest paths problem?

I was wondering to know whether Dijkstra's algorithm can find the optimal solution for a weighted and directed shortest paths problem where: 1) for each arc $(i,j)$, $i>j$ and 2) it is not always ...
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### Derivations for two formulae for obtaining optimal dual variable values from the optimal primal tableau

We're being taught Industrial Engineering and Operations Research for the first time this semester. Referring to the book by Hamdy A. Taha, I noticed the mention of two formulae for swiftly obtaining ...
I have tried to solve an optimization problem (an MINLP) to minimize the number of items which need to be stored. The objective function is as follows: \min \quad z = \sum_{i=1}^{n} \, \color{blue} {...