TL;DR
This paper proposes an exact parametric dynamic programming algorithm that achieves polynomial oracle complexity when the node cost functions belong to a fixed degree weak Chebyshev space, a broad functional class that includes piecewise polynomials.
A unified framework, based on decision diagrams, is proposed that serves both to solve the associated optimization problems and to construct ideal conic quadratic extended formulations of the closure of the convex hull of the underlying mixed-integer set.
We consider the problem of minimizing a sparse quadratic function over the unit hypercube. In binary quadratic programming, treewidth of the interaction graph is a central parameter for tractability: bounded treewidth yields polynomial-time solvability. Motivated by this fact, we investigate whether treewidth plays a s...
We study mixed-integer quadratic fractional optimization problems with binary and continuous box-constrained variables. The objective is the ratio of two quadratic functions, a structure that arises naturally in portfolio selection, signal processing, and data analytics. We propose an exact algorithm based on Dinkelbac...
It is shown that a class of binary optimization problems with complex non-quadratic objectives or constraints can be reformulated as multi-objective quadratic unconstrained binary optimization problems and evaluated classically on Pareto-optimal candidates rather than encoded as penalties.
We give an exact algorithm for continuous separable convex quadratic programming with an integer equality matrix and nonnegative variables. The number of rational arithmetic operations and comparisons is polynomial in the dimensions and the encoding length of the constraint matrix, independently of the right-hand side,...
Greedy algorithms efficiently approximate combinatorial optimization problems, but their guarantees weaken when feasibility couples combinatorial structure with global physical constraints. We study monotone nondecreasing supermodular minimization over the bases of a graphic greedoid under physics-induced constraints....
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