Deep learning (DL) has become a successful approach to solving various problems, especially within computer vision, and has applications in numerous areas. Convolutional Neural Networks (CNNs), which consist of multiple layers, are commonly used in image processing and have shown superior prediction performance compared to previous methods. Semi-Infinite Programming (SIP) is a class of problems where a restricted count of variables is subject to infinite constraints. This study proposes an optimization model based on SIP to prune an ensemble of CNNs by considering both squared loss and Shannon Entropy functions. The objective is to balance the ensemble’s accuracy and diversity, which is optimized by defining the trade-off parameter as the index of an infinite index set of constraints. To avoid the dependence on pruning size, each network in the ensemble is assigned weights that become variables in the optimization model. A norm constraint is added to sparsify the weights and determine the pruning size. The proposed mathematical model is evaluated on popular image processing datasets, CIFAR-10 and MNIST, and yields promising results.
The Black-and-White Coloring (BWC) problem seeks a coloring of a graph’s vertices, minimizing the number of edges with endpoints of different colors, given a fixed number of black and white vertices. This problem is known to be NP-complete. We prove that no polynomial-time algorithm can achieve an additive approximation for this problem, unless P = NP.
As is well-known, collinearity in data sets has long been recognized as a factor that significantly influences data mining processes in various aspects, particularly in high-dimensional cases. To effectively address this issue, especially in contemporary models where collinearity often arises, we aim to modify a classic data compression technique. Specifically, our study focuses on the least-squares model of the nonnegative matrix factorization (NMF) problem, with the goal of improving the condition number of the decomposition elements. This improvement is intended to reduce the collinearity level in the resulting output matrices. Our approach involves embedding penalty terms into the traditional NMF model, integrating two recently proposed penalty frameworks to form a hybrid model. To solve this extended model, we develop a revised version of the Hestenes–Stiefel (HS) conjugate gradient (CG) algorithm, by modifying the classic parameter of the algorithm while ensuring that its anti-jamming property is preserved. We further discuss how such a modification reinforces the anti-jamming characteristic of the HS method. We test our theoretical claims on both standard benchmark problems and randomly generated test problems, evaluating the results to assess the effectiveness of our approach. The findings generally demonstrate that the proposed modifications yield promising results.
This paper proposes an efficient Nonlinear Model Predictive Control (NMPC) framework for precise trajectory tracking of quadrotor Unmanned Aerial Vehicles (UAVs). The quadrotor’s nonlinear dynamics are modeled using the Euler-Lagrange formulation, capturing six degrees of freedom while considering system constraints. The NMPC optimizes performance via a quadratic cost function over a finite prediction horizon, integrating advanced trajectory generation and real-time computation capabilities. Simulation results validate the proposed controller’s ability to track accurately across challenging scenarios, maintain stability under disturbances, and ensure computational efficiency for real-time applications. This work provides a practical and robust solution to key challenges in autonomous UAV control.
In this work, we will present derivative-free versions of the Local Simplex Algorithm (LSA) for finding a local minimum of a real-valued concave function which can be smooth or non-smooth over two types of polyhedrons: box-constraints, linear equality constraints and non-negative variables. Finally, we give some numerical examples and preliminary numerical experiments which illustrate the algorithm and we discuss some extensions.
