Cinar Ari

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math.OC2026

Hidden Convexity via Symmetric Displacement Covers: Mixed-Integer Quadratic Programming and Integer Cubic Programming in Fixed Dimension

Cinar Ari, Robert Hildebrand

We give exact polynomial-time algorithms in fixed dimension for mixed-integer quadratic programming over arbitrary rational polyhedra and for integer cubic programming over bounded…

math.OC2026

Bounded Integer Quadratic Programming through Parallelepiped Covers and Discrete Convic Optimization

Cinar Ari, Robert Hildebrand

We give an exact algorithm for minimizing an arbitrary rational quadratic polynomial $x^{T} Q x + c^{T} x + γ$ over the integer points of a bounded rational polyhedron $\{x : Ax \le b\…

math.OC2026

Integer Maximization over $ℓ_{p}$ Balls: Hardness and Exact Algorithms

Cinar Ari, Robert Hildebrand

We study the problem of maximizing a linear function over the integer points of an origin-centered $ℓ_{p}$ ball, which we call \BallIPp{p}. For every fixed integer $p \geq 2$ , we pro…

math.OC2026

Curvature batching for integer and mixed-integer quadratic programming

Cinar Ari, Robert Hildebrand

We give an explicit algorithm for integer quadratic programming with running time $(n L)^{O (n^{2})} poly (ϕ)$ , where $n$ is the number of variables, $L$ bounds the absolute en…

Hidden Convexity via Symmetric Displacement Covers: Mixed-Integer Quadratic Programming and Integer Cubic Programming in Fixed Dimension

Bounded Integer Quadratic Programming through Parallelepiped Covers and Discrete Convic Optimization

Integer Maximization over ℓp​ Balls: Hardness and Exact Algorithms

Curvature batching for integer and mixed-integer quadratic programming

Integer Maximization over $ℓ_{p}$ Balls: Hardness and Exact Algorithms