# Questions tagged [integer-programming]

Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.

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### Why are optimization problems often called “programs”?

**10**

**1**answer

### Condition for existence of certain lattice points on polytopes

**8**

**1**answer

### Proving that a binary matrix is totally unimodular

**8**

**1**answer

### On linear integer inequalities with infinitely many solutions

**8**

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### What is the probability of interpolating the Tutte polynomial of a planar graph from the values at the two hyperbolas?

**7**

**1**answer

### Complexity of integer programming with added predicates

**6**

**2**answers

### is there a solution to this linear Diophantine system?

**6**

**1**answer

### Algorithm that solves every Mixed Integer Linear Program (to optimality)?

**6**

**1**answer

### Existence of nonnegative solution in diophantine linear equations system with non negative coefficents

**6**

**1**answer

### Is a Parametric Integer Linear Programming Problem eventually quasi-polynomial?

**6**

**1**answer

### Speed up Linear programming

**6**

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### Efficient solutions to general Bézout’s identity $a_1 b_1 + \dots + a_n b_n = 1$

**5**

**1**answer

### Minimum distance between adjacent concentric circles that cross integer lattice points

**5**

**2**answers

### Some weird “system” of inequalities in nonnegative integers.

**5**

**1**answer

### Is Binary Integer Linear Programming solvable in polynomial time?

**5**

**2**answers

### Area of a lattice polygon in terms of its width

**5**

**1**answer

### Hermite normal form in families

**5**

**1**answer

### Maximize the determinant of Boolean combinations of positive definite matrices

**5**

**1**answer

### Algorithm to minimally connect line segments in Euclidean plane

**5**

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### Lattice paths in polytopes

**4**

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### Lattice points close to a line

**4**

**2**answers

### What are the definable sets in Skolem arithmetic?

**4**

**1**answer

### On necessary condition for no integer points in polytope

**4**

**2**answers

### Simplified knapsack problem

**4**

**1**answer

### Symmetry of the integer gap

**4**

**0**answers

### Choice of MIP (mixed integer programming) solver

**4**

**0**answers

### Matching a binary matrix

**4**

**0**answers

### Domination in Nice Lattices

**3**

**2**answers

### Integer programming of free energy

**3**

**1**answer

### Under what conditions does an Integer Programming problem run in polynomial time?

**3**

**2**answers

### Sherali-Adams relaxation

**3**

**1**answer

### An interesting problem which I think only needs elementary number theory

**3**

**2**answers

### Finding closest point to a set of circles

**3**

**1**answer

### When is a triangular matrix totally unimodular?

**3**

**1**answer

### Sufficient condition for solvability of linear diophantine system

**3**

**1**answer

### Separation of Anti-Hole Inequality

**3**

**1**answer

### Partially optimal solutions in integer linear programming

**3**

**2**answers

### Equality constraints in mixed-integer optimization

**3**

**1**answer

### Name search for special Linear Integer Program

**3**

**0**answers

### Optimally placing rectangles with obstacles

**3**

**0**answers

### The complexity of an optimization problem involving sum of binomial coefficients

**3**

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### Lenstra's integer programming algorithm: Finding a lattice point “near the center”

**3**

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### Reference request: how to find the k'th best solution to the 1-0 knapsack problem?

**3**

**0**answers

### About the partial expectation polynomials in the Interlacing-I paper and perfect matchings

**3**

**0**answers

### Beating Kadane's Algorithm

**3**

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### 0,1 solution to system of linear integer equations

**3**

**2**answers

### SDP relaxation vs LP relaxation

**2**

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### On special type polynomial inequalities over integers

**2**

**1**answer

### Numbers that are the sum of 2 distinct nonzero squares in exactly 1 way [closed]

**2**

**2**answers