Superposition relaxation creates separable estimators for factorable functions that are tighter than McCormick relaxations in numerical tests while providing convergence guarantees.
Mathematical Programming 10(1), 147–175 (1976)
8 Pith papers cite this work. Polarity classification is still indexing.
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New nonlinear formulations for geometric packing problems, solved with FICO Xpress and SCIP, produce improved and first-known solutions for several variants.
A complete linear inequality description and volume formula are derived for the convex hull of the graph of a monomial on a nonnegative box with at most one positive lower bound.
PALM-Mean combines sign-aware piecewise-linear relaxations of locally important kernel terms with closed-form analytic bounds on the rest inside a reduced-space branch-and-bound framework, yielding valid lower bounds and ε-global convergence for GP posterior mean optimization.
Establishes a tight double-exponential lower bound for high-multiplicity bin packing parameterized by number of distinct item types d, showing no |I|^{2^{o(d)}} algorithm exists unless ETH fails, via a novel 3-SAT reduction to an ILP with O(log n) variables.
The reverse polar of visible points from an infeasible point coincides with that of the full feasible region, enabling tighter valid cuts for MINLPs described by a single non-convex constraint intersected with a convex set.
A scalable verification framework for neural control barrier functions uses linear bound propagation on network gradients combined with McCormick relaxations to certify safety conditions for control-affine systems.
Extends a 2023 result on relaxation dominance in multilinear optimization to broader linearizations, supplies a simpler proof, and proves that the intersection with the extended flower relaxation is equivalent in strength.
citing papers explorer
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Relaxation via Separable Estimators: Arithmetic and Implementation
Superposition relaxation creates separable estimators for factorable functions that are tighter than McCormick relaxations in numerical tests while providing convergence guarantees.
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Out-of-the-Box Global Optimization for Packing Problems: New Models and Improved Solutions
New nonlinear formulations for geometric packing problems, solved with FICO Xpress and SCIP, produce improved and first-known solutions for several variants.
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On the convex hull of the graph of a simple monomial
A complete linear inequality description and volume formula are derived for the convex hull of the graph of a monomial on a nonnegative box with at most one positive lower bound.
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An Efficient Spatial Branch-and-Bound Algorithm for Global Optimization of Gaussian Process Posterior Mean Functions
PALM-Mean combines sign-aware piecewise-linear relaxations of locally important kernel terms with closed-form analytic bounds on the rest inside a reduced-space branch-and-bound framework, yielding valid lower bounds and ε-global convergence for GP posterior mean optimization.
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A Tight Double-Exponentially Lower Bound for High-Multiplicity Bin Packing
Establishes a tight double-exponential lower bound for high-multiplicity bin packing parameterized by number of distinct item types d, showing no |I|^{2^{o(d)}} algorithm exists unless ETH fails, via a novel 3-SAT reduction to an ILP with O(log n) variables.
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Visible points, the separation problem, and applications to MINLP
The reverse polar of visible points from an infeasible point coincides with that of the full feasible region, enabling tighter valid cuts for MINLPs described by a single non-convex constraint intersected with a convex set.
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Scalable Verification of Neural Control Barrier Functions Using Linear Bound Propagation
A scalable verification framework for neural control barrier functions uses linear bound propagation on network gradients combined with McCormick relaxations to certify safety conditions for control-affine systems.
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Relaxation strength for multilinear optimization: McCormick strikes back
Extends a 2023 result on relaxation dominance in multilinear optimization to broader linearizations, supplies a simpler proof, and proves that the intersection with the extended flower relaxation is equivalent in strength.