Related papers: Optimization techniques for modeling with piecewis…
Mixed integer linear programming (MILP) has seen a sharp rise in use for engineering optimization applications in recent years. Even for initially non-linear problems, it is often the method of choice. Then, the non-linear functions have to…
This paper addresses the problem of tightening the mixed-integer linear programming (MILP) formulation for continuous piecewise linear (CPWL) approximations of data sets in arbitrary dimensions. The MILP formulation leverages the…
Several techniques were proposed to model the Piecewise linear (PWL) functions, including convex combination, incremental and multiple choice methods. Although the incremental method was proved to be very efficient, the attention of the…
The load pick-up (LPP) problem searches the optimal configuration of the electrical distribution system (EDS), aiming to minimize the power loss or provide maximum power to the load ends. The piecewise linearization (PWL) approximation…
In this paper, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex hull representation. Based on the solution of the PPR, we also present a MILP…
Piecewise regression is a versatile approach used in various disciplines to approximate complex functions from limited, potentially noisy data points. In control, piecewise regression is, e.g., used to approximate the optimal control law of…
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…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…
In this paper, we investigate the constraint typology of mixed-integer linear programming MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life scheduling, routing, planning,…
Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving,…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
This article describes the methodology for formulating and solving optimal pump scheduling problems with variable-speed pumps (VSPs) as mixed integer linear programs (MILPs) using piece-linear approximations of the network components. The…
Real-world scenarios are characterized by timing uncertainties, e.g., delays, and disturbances. Algorithms with temporal robustness are crucial in guaranteeing the successful execution of tasks and missions in such scenarios. We study…