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
39 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
75 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
38 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
84 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
404 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
176 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
224 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
521 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 ...