Related papers: Branch-and-Price for a Class of Nonconvex Mixed-In…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Challenges in last-mile delivery have encouraged innovative solutions like crowdsourced delivery, where online platforms leverage the services of drivers who occasionally perform delivery tasks for compensation. A key challenge is that…
Non-convex, nonlinear gas network optimization models are used to determine the feasibility of flows on existing networks given constraints on network flows, gas mixing, and pressure loss along pipes. This work improves two existing gas…
Two-stage stochastic integer programs provide a powerful framework for modeling decision-making under uncertainty, but they are notoriously difficult to solve at scale due to their high dimensionality and intrinsic nonconvexity.…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the…
The optimal selection, sizing, and location of small-scale technologies within a grid-connected distributed energy system (DES) can contribute to reducing carbon emissions, consumer costs, and network imbalances. This is the first study to…
Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of…
Strategic bidding problems in electricity markets are widely studied in power systems, often by formulating complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to…
This paper presents an approach to joint wireless and computing resource management in slice-enabled metaverse networks, addressing the challenges of inter-slice and intra-slice resource allocation in the presence of in-network computing.…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
Embedding deep neural networks (NNs) into mixed-integer programs (MIPs) is attractive for decision making with learned constraints, yet state-of-the-art monolithic linearisations blow up in size and quickly become intractable. In this…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…
Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…