Questions tagged [numerical-issues]

For questions on problems that come from a finite representation of real numbers.

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3 votes
1 answer
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What approximation is guarantees when solving an LP with floating-point numbers?

Given a linear program $$\begin{align} \text{maximize} \quad & c^{T}x \\ \text{s.t.} \quad & A x \leq b \end{align} $$ I can solve it exactly in polynomial time, using e.g. interior-point ...
Erel Segal-Halevi's user avatar
4 votes
1 answer
141 views

Applications where a very high numeric accuracy is required

In numeric algorithms, an important parameter is the accuracy. Usually, the run-time of such algorithms, when they are required to return an $\epsilon$-approximate solution, is a function of $1/\...
Erel Segal-Halevi's user avatar
1 vote
0 answers
87 views

Numerical infeasibility for moving numbers along some specific conversion edges to get maximal number on target node from some starter node

I have a problem that can be represented as an optimization problem. Sometimes, solver engines report infeasible depending on the parameters I have at hand. The root cause is numeric ranges. ...
Dzmitry Lahoda's user avatar
2 votes
1 answer
336 views

Poorly conditioned quadratic programming with "simple" linear constraints

I have many quadratic programming problems of the following form: $$\min_{x\in\mathbb{R}^n} { \tfrac{1}{2} {\lVert Cx-d \rVert}^2} $$ $$\textrm{s.t.}\ x_1\le 0,\ x_n\le 0,\ x_n\le a_1^\top x_{1:n-1},\ ...
cfp's user avatar
  • 259
3 votes
2 answers
363 views

Impact of soft constraints in MILP

I'm wondering about the impact of soft constraints, since no one mentioned that in Soft constraints and hard constraints. My team makes all the constraints soft in MILP, so that a feasible solution ...
Edward's user avatar
  • 391
8 votes
4 answers
826 views

Detect Numerical Instability with Large-scale optimization problems

We run large-scale optimization problems regularly. They have thousand of variables and tens of thousands of constraints. Those optimization problems often get numerically instable. In those cases, we ...
pqrz's user avatar
  • 470
1 vote
2 answers
1k views

Docplex Error: Model has non-convex objective

My objective function is $\frac{1}{2}w^{T}Vw - P^{T}w$ with $V$ a covariance matrix (hence semidefinite positive), $P$ a column vector and $w$ a vector of semi-continuous variables. Given that the ...
FredNgu's user avatar
  • 157
6 votes
0 answers
223 views

Provide basic solution to CLP

I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
Arjan Dijkstra's user avatar
9 votes
0 answers
200 views

Ill-conditioned LP in Benders decomposition

I have implemented a Benders decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the subproblem dual LP. As you can see below, the coefficients ...
Mauricio Zambon's user avatar
14 votes
2 answers
237 views

Solver rounding precision vs programming language rounding precision

Often times I have this issue. For example, I need to have a non-negative coefficient, say $c_0$, in my optimization problem (otherwise the problem is not convex). Moreover, to obtain this $c_0$ I ...
independentvariable's user avatar