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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3
votes
1answer
71 views

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 ...
1
vote
0answers
42 views

The different behavior of the solvers to dial with MINLP problem

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} {...
0
votes
1answer
47 views

What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?

Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
6
votes
3answers
140 views

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 ...
4
votes
1answer
77 views

the set of optimal solutions of a linear programming (LP) problem as a mapping of right-hand side

Consider a linear programming (LP) problem \begin{align} M(b) \in \arg\min_x \{ c^\top x : Ax=b, x \ge 0 \}. \end{align} Suppose the LP is feasible and bounded for all values of $b$. We know that $M(...
3
votes
1answer
45 views

Is Multidisciplinary Design Optimization / Collaborative Optimization used anywhere outside of the Mechanical Engineering context?

I recently stumbled across the concept of Multidisciplinary Design Optimization (MDO), sometimes referred to as Multi-Disciplinary Optimization or Multidisciplinary Systems Design Optimization (MSDO), ...
3
votes
1answer
118 views

Radial unboundedness vs convexity

We have a simple problem, namely minimizing: $$f(x) = x_1^2 + x_2^2 - x_1.$$ The gradient is $$\nabla f(x) = \begin{bmatrix} 2x_1 - 1 \\ 2x_2 \end{bmatrix},$$ hence the unique stationary point is: $...
3
votes
0answers
41 views

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 ...
9
votes
1answer
88 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
446 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 ...
12
votes
1answer
204 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
2k 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
417 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
906 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 ...