I know it depends on the specific problem instance, but approximately how large of an MIP problem can we write and still be guaranteed that an optimization solver will find a solution? For instance, if we have a mixed integer program with 1,000 variables and 1,000 constraints, can we be guaranteed that no matter what the variables and constraints are, modern optimization software will be able to spit out a solution in a reasonable time frame (defined as 1 month or less on a standard computer)? What about 1 million variables and constraints, or a billion variables and a million constraints, etc.
2026-03-27 23:22:32.1774653752
How many variables and constraints can modern mixed integer programming solvers handle?
123 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in OPTIMIZATION
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- optimization with strict inequality of variables
- Gradient of Cost Function To Find Matrix Factorization
- Calculation of distance of a point from a curve
- Find all local maxima and minima of $x^2+y^2$ subject to the constraint $x^2+2y=6$. Does $x^2+y^2$ have a global max/min on the same constraint?
- What does it mean to dualize a constraint in the context of Lagrangian relaxation?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Building the model for a Linear Programming Problem
- Maximize the function
- Transform LMI problem into different SDP form
Related Questions in LINEAR-PROGRAMMING
- Proving dual convex cone property
- Linear algebra: what is the purpose of passive transformation matrix?
- Building the model for a Linear Programming Problem
- Show that $ \ x_ 0 \ $ cannot be an optimal solution
- Is there any way to model this situation in integer programming?
- How to Solve a Linear Programming Problem in $n$ Dimension Space?
- How to solve a linear program without any given data?
- Constraints for continuous path within graph with at least one obligatory node in path
- Select the smallest strict positive value from a list of variables in a linear program.
- How to add nonnegative constraint to an LP problem
Related Questions in INTEGER-PROGRAMMING
- Dynamic programming for Knapsack problem
- Find minimum $x+y+z$ given $3x=4y=7z$ and $x, y, z \in \mathbb N^+$
- conditional constraints -Integer programming
- Integer programming proof: If an LP is unbounded then the IP is unbounded
- Integrality gap of maximum weighted clique
- "No two values are the same" constraint in linear programming
- Looking for some information on applications of integer linear programming
- How to find the number of possible ways to climb the staircase
- Consecutive binary variables, without using auxiliary variables
- Job Shop Optimization -- Minimize Total Completion Time
Related Questions in PROGRAMMING
- Neyman-Pearson precision problem
- How to find the number of possible ways to climb the staircase
- How many cells are expected?
- Help understanding this numerical surface integration technique?
- Random tree generation probability problem
- What math do I need to learn to create a general equation solver?
- Non-commutative sum?
- Basel problem, numerically
- Proof of correctness (loop invariant) for Fibonacci numbers
- Logic proof verification - Hoare
Related Questions in MIXED-INTEGER-PROGRAMMING
- Is this statement implying that a binary variable can be between 0 and 1?
- System of Linear Inequalities to create feasible solution $y=\min(x_1,x_2)$
- Ensure (or limit) consecutive presence of variable in MILP
- MILP constraints with truth table
- Is there any mixed integer linear programming module capable of handling integer variables exactly?
- Solve $n * \lceil{\frac{R}{T}}\rceil - \lceil{\frac{R*n}{T} - \frac{x*n}{T}}\rceil = \frac{x * n}{C}$ for x and n, $n \in Z^+$ and $x,R,T,C \in R^+$
- Table formulation in Mixed Integer Programming
- How to optimize for following cost function?
- How to linearize the following constraint? (a summation of a product of a integer with a bounded continuous variable)
- Convert nonlinear constraint to linear constraints for mixed-integer linear programming in MATLAB
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?