In this work, we revisit binary polynomial optimization (BPO) problems with limited treewidth of the associated graph. We provide alternate proofs of the exactness of a reformulated linear program (LP) with O(n.2^d) variables, n being the number of variables and d being the treewidth of the associated graph. The first proof relies on expressing any ...

The representation of a function in a higher-dimensional space, often referred to as lifting, can be used to reduce complexity. We investigate how lifting affects the convergence properties of Newton-type methods. For the first time, we conduct a systematic comparison of several lifting strategies on a set of 40 optimal control problems. In addition, we ...

This paper proposes a context-aware multi-uncertainty-set distributionally robust chanceconstrained DC optimal power flow model. Meteorological features are projected to partition the non-convex error support into a context-dependent decomposition of conditional local ambiguity sets, with conditional weights inferred via kernel regression. The minimax problem is reformulated int...

We study time-of-use pump scheduling to deliver a required volume using a finite set of pump combinations with empirical flow–power performance, subject to per-shift caps on pump switches. We prove a structural theorem: partitioning the horizon into maximal intervals with constant tariff and shift (atoms), there always exists an optimal schedule with at most one ...

In this paper, we develop a stochastic set-valued optimization (SVO) framework tailored for robust machine learning. In the SVO setting, each decision variable is mapped to a set of objective values, and optimality is defined via set relations. We focus on SVO problems with hyperbox sets, which can be reformulated as multi-objective optimization (MOO) problems ...