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This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to "modern" methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.

Nonlinear programming --- Programming (Mathematics) --- Convex optimization. --- Linear and quadratic constraints. --- Nondifferential and global optimization. --- Optimality conditions. --- Penalty methods.

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In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990's. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.

Metric spaces. --- G-spaces. --- Hadamard matrices. --- Combinatorial analysis --- Combinatorial designs and configurations --- Matrices --- Geodesic spaces --- Spaces, G --- Spaces, Geodesic --- G-structures --- Metric spaces --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Convex analysis. --- Convex optimization. --- Geodesic convexity. --- Hadamard space. --- Metric geometry. --- Nonpositive curvature.

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Machine learning is extending its applications in various fields, such as image processing, the Internet of Things, user interface, big data, manufacturing, management, etc. As data are required to build machine learning networks, sensors are one of the most important technologies. In addition, machine learning networks can contribute to the improvement in sensor performance and the creation of new sensor applications. This Special Issue addresses all types of machine learning applications related to sensors and imaging. It covers computer vision-based control, activity recognition, fuzzy label classification, failure classification, motor temperature estimation, the camera calibration of intelligent vehicles, error detection, color prior model, compressive sensing, wildfire risk assessment, shelf auditing, forest-growing stem volume estimation, road management, image denoising, and touchscreens.

star image --- image denoising --- reinforcement learning --- maximum likelihood estimation --- mixed Poisson–Gaussian likelihood --- machine learning-based classification --- non-uniform foundation --- stochastic analysis --- vehicle–pavement–foundation interaction --- forest growing stem volume --- coniferous plantations --- variable selection --- texture feature --- random forest --- red-edge band --- on-shelf availability --- semi-supervised learning --- deep learning --- image classification --- machine learning --- explainable artificial intelligence --- wildfire --- risk assessment --- Naïve bayes --- transmission-line corridors --- image encryption --- compressive sensing --- plaintext related --- chaotic system --- convolutional neural network --- color prior model --- object detection --- piston error detection --- segmented telescope --- BP artificial neural network --- modulation transfer function --- computer vision --- intelligent vehicles --- extrinsic camera calibration --- structure from motion --- convex optimization --- temperature estimation --- BLDC --- electric machine protection --- touchscreen --- capacitive --- display --- SNR --- stylus --- laser cutting --- quality monitoring --- artificial neural network --- burr formation --- cut interruption --- fiber laser --- semi-supervised --- fuzzy --- noisy --- real-world --- plankton --- marine --- activity recognition --- wearable sensors --- imbalanced activities --- sampling methods --- path planning --- Q-learning --- neural network --- YOLO algorithm --- robot arm --- target reaching --- obstacle avoidance

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Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Interpolation. --- Smoothing (Numerical analysis) --- Smoothing (Statistics) --- Curve fitting. --- Splines. --- Spline theory. --- Spline functions --- Approximation theory --- Interpolation --- Joints (Engineering) --- Mechanical movements --- Harmonic drives --- Fitting, Curve --- Numerical analysis --- Least squares --- Statistics --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Graphic methods --- Accuracy and precision. --- Affine space. --- Affine variety. --- Algorithm. --- Approximation. --- Arbitrarily large. --- B-spline. --- Banach space. --- Bernstein polynomial. --- Bifurcation theory. --- Big O notation. --- Birkhoff interpolation. --- Boundary value problem. --- Bézier curve. --- Chaos theory. --- Computation. --- Computational problem. --- Condition number. --- Constrained optimization. --- Continuous function (set theory). --- Continuous function. --- Control function (econometrics). --- Control theory. --- Controllability. --- Convex optimization. --- Convolution. --- Cubic Hermite spline. --- Data set. --- Derivative. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Directional derivative. --- Discrete mathematics. --- Dynamic programming. --- Equation. --- Estimation. --- Filtering problem (stochastic processes). --- Gaussian quadrature. --- Gradient descent. --- Gramian matrix. --- Growth curve (statistics). --- Hermite interpolation. --- Hermite polynomials. --- Hilbert projection theorem. --- Hilbert space. --- Initial condition. --- Initial value problem. --- Integral equation. --- Iterative method. --- Karush–Kuhn–Tucker conditions. --- Kernel method. --- Lagrange polynomial. --- Law of large numbers. --- Least squares. --- Linear algebra. --- Linear combination. --- Linear filter. --- Linear map. --- Mathematical optimization. --- Mathematics. --- Maxima and minima. --- Monotonic function. --- Nonlinear programming. --- Nonlinear system. --- Normal distribution. --- Numerical analysis. --- Numerical stability. --- Optimal control. --- Optimization problem. --- Ordinary differential equation. --- Orthogonal polynomials. --- Parameter. --- Piecewise. --- Pointwise. --- Polynomial interpolation. --- Polynomial. --- Probability distribution. --- Quadratic programming. --- Random variable. --- Rate of convergence. --- Ratio test. --- Riccati equation. --- Simpson's rule. --- Simultaneous equations. --- Smoothing spline. --- Smoothing. --- Smoothness. --- Special case. --- Spline (mathematics). --- Spline interpolation. --- Statistic. --- Stochastic calculus. --- Stochastic. --- Telemetry. --- Theorem. --- Trapezoidal rule. --- Waypoint. --- Weight function. --- Without loss of generality.

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Machine learning is extending its applications in various fields, such as image processing, the Internet of Things, user interface, big data, manufacturing, management, etc. As data are required to build machine learning networks, sensors are one of the most important technologies. In addition, machine learning networks can contribute to the improvement in sensor performance and the creation of new sensor applications. This Special Issue addresses all types of machine learning applications related to sensors and imaging. It covers computer vision-based control, activity recognition, fuzzy label classification, failure classification, motor temperature estimation, the camera calibration of intelligent vehicles, error detection, color prior model, compressive sensing, wildfire risk assessment, shelf auditing, forest-growing stem volume estimation, road management, image denoising, and touchscreens.

Technology: general issues --- History of engineering & technology --- star image --- image denoising --- reinforcement learning --- maximum likelihood estimation --- mixed Poisson–Gaussian likelihood --- machine learning-based classification --- non-uniform foundation --- stochastic analysis --- vehicle–pavement–foundation interaction --- forest growing stem volume --- coniferous plantations --- variable selection --- texture feature --- random forest --- red-edge band --- on-shelf availability --- semi-supervised learning --- deep learning --- image classification --- machine learning --- explainable artificial intelligence --- wildfire --- risk assessment --- Naïve bayes --- transmission-line corridors --- image encryption --- compressive sensing --- plaintext related --- chaotic system --- convolutional neural network --- color prior model --- object detection --- piston error detection --- segmented telescope --- BP artificial neural network --- modulation transfer function --- computer vision --- intelligent vehicles --- extrinsic camera calibration --- structure from motion --- convex optimization --- temperature estimation --- BLDC --- electric machine protection --- touchscreen --- capacitive --- display --- SNR --- stylus --- laser cutting --- quality monitoring --- artificial neural network --- burr formation --- cut interruption --- fiber laser --- semi-supervised --- fuzzy --- noisy --- real-world --- plankton --- marine --- activity recognition --- wearable sensors --- imbalanced activities --- sampling methods --- path planning --- Q-learning --- neural network --- YOLO algorithm --- robot arm --- target reaching --- obstacle avoidance