Related papers: Relax-Tighten-Round Algorithm for Optimal Placemen…
Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
Efficient exact algorithms for Discrete Optimization (DO) rely heavily on strong primal and dual bounds. Relaxed Decision Diagrams (DDs) provide a versatile mechanism for deriving such dual bounds by compactly over-approximating the…
An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…
Contention resolution schemes (or CR schemes), introduced by Chekuri, Vondrak and Zenklusen, are a class of randomized rounding algorithms for converting a fractional solution to a relaxation for a down-closed constraint family into an…
Determining the maximum demand a water distribution network can satisfy is crucial for ensuring reliable supply and planning network expansion. This problem, typically formulated as a mixed-integer nonlinear program (MINLP), is…
This paper investigates the water network's potential ability to provide demand response services to the power grid under the framework of a distribution-level water-energy nexus (micro-WEN). In particular, the hidden controllability of…
AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global…
Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due…
This paper introduces a novel method for numerically stabilizing sequential continuous adjoint flow solvers utilizing an elliptic relaxation strategy. The proposed approach is formulated as a Partial Differential Equation (PDE) containing a…
The Unit Commitment problem with AC power flow constraints (UC-ACOPF) is a non-convex mixed-integer nonlinear programming (MINLP) problem encountered in power systems. Its combination of combinatorial complexity and non-convex nonlinear…
We present an accelerated relax-and-round algorithm for concave coverage problems, which generalize the classic maximum coverage problem. Building on the relax-and-round framework of Barman et al. [STACS 2021], we propose two significant…
We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the…
We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes…
Mixing of binary fluids by moving stirrers is a commonplace process in many industrial applications, where even modest improvements in mixing efficiency could translate into considerable power savings or enhanced product quality. We propose…
The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical…