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Nonlinear expressions are often approximated by piecewise affine (PWA) functions to simplify analysis or reduce computational costs. To reduce computational complexity, multivariate functions can be represented as compositions of functions…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
We propose two optimization-based heuristics for structure selection and identification of PieceWise Affine (PWA) models with exogenous inputs. The first method determines the number of affine sub-models assuming known model order of the…
By exploiting the correlation between the structure and the solution of Mixed-Integer Linear Programming (MILP), Machine Learning (ML) has become a promising method for solving large-scale MILP problems. Existing ML-based MILP solvers…
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 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.…
Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
Upgradeability problems are a critical issue in modern operating systems. The problem consists in finding the "best" solution according to some criteria, to install, remove or upgrade packages in a given installation. This is a difficult…
In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. The training data are generated uniformly in the domain of interest, consisting of…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Proportional-integral-derivative (PID) control, the most common control strategy in the industry, always suffers from health problems resulting from external disturbances, improper tuning, etc. Therefore, there have been many studies on…
We introduce a new method, stepwise method for solving optimal con- trol problems. Our first motivation for new approach emanate from limi- tations on continuous time control functions in PMP. Practically in most of the real world models,…
The split covariance intersection filter (split CIF) is a useful tool for general data fusion and has the potential to be applied in a variety of engineering tasks. An indispensable optimization step (referred to as w-optimization) involved…
Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…
This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…
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…
We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…