# 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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### Integer linear programming (ILP) formulation of connectivity of induced subgraph

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### How do you refer to the feasible set of solutions to a mixed-integer program?

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### Gröbner basis via integer programming

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### What are all the possibilities of $A$ s.t. $\det(A)=k$?

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### How do I solve this integer programming problem with non convex constraints?

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

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### Feasibility Criteria in Integer Linear Programming

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### Integer programming problem

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### Modelling exact unions of polytopes in homogeneous case?

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### Mixed integer formulation of union of polytopes?

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### Convex integer program with totally unimodular constraints

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### Algorithm for (binary) integer programming

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

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### Fast certficate of negativity for objective value of mixed-integer linear program

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### Smallest integer lattice point by box measure in a polytope?

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

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### Minimizing sum of ratio of linear functions (Sum of Linear Ratios Problem)

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### When are quadratic integer programs “easy to solve”?

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### How good is the LP relaxation?

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

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### How to solve such integer program problem?

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### How to minimize n-polytope's bounding box with linear transformation?

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### Relax a rectangular linear assignment problem

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### Feasibility Mixed integer Linear programming with quadratic constraints?

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### On OR condition in Linear Programming with exponentially many constraints [closed]

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### Clarification on FPTAS optimization in a paper

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### Convex integer programming on totally unimodular polytope?

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### Finding a point in the relative interior of the convex hull of a set of integer-valued vectors

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### What does Lenstra's MILP do?

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### Bit complexity of Barvinok's algorithm

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### On software for ILP

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### Discrete primal-duality in optimization

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### Detection of gaps in binary vector through linear methods

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

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

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### Gap in Successive minima on lattice spanned by rational and integer combination of integer vectors

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### Integer points spanned by real, rational and integer combination of integer vectors

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### Making a polyhedron integral by selecting value for a specific co-ordinate of constraint vector

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### Feasibility of constrained multivariable diophantine equations

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

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### Equality constraints in mixed-integer optimization

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### MIQP formulation in L0 norm optimization

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### Lot Sizing Problem: How to add these cuts efficiently

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### Optimally placing rectangles with obstacles

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### Does this simple non-convex problem involving discrete phase shifts have an exact solution?

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### Integer programming of free energy

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### Lattice question

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### A seemingly easy integer programming question

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### Lattice paths in polytopes

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