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Programming (Mathematics) --- Linear Programming --- Business mathematics --- 519.85 --- transport --- Linear programming --- geheel --- dynamisch --- integer --- programmeren --- economie --- simplex --- problemen --- spel --- lineaire programmering --- toewijzing --- niet-lineair --- kuhn-tucker --- Mathematical programming --- Goal programming --- Algorithms --- Functional equations --- Mathematical optimization --- Operations research --- Matrices --- Production scheduling --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Finance --- Mathematics --- 519.85 Mathematical programming --- Linear programming.

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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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Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function.The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs.Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.

Interior-point methods. --- Mathematical optimization. --- Programming (Mathematics). --- Mathematical optimization --- Interior-point methods --- Programming (Mathematics) --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Mathematical programming --- Goal programming --- Algorithms --- Functional equations --- Operations research --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Simulation methods --- System analysis --- 519.85 --- 681.3*G16 --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.85 Mathematical programming --- Accuracy and precision. --- Algorithm. --- Analysis of algorithms. --- Analytic function. --- Associative property. --- Barrier function. --- Binary number. --- Block matrix. --- Combination. --- Combinatorial optimization. --- Combinatorics. --- Complexity. --- Conic optimization. --- Continuous optimization. --- Control theory. --- Convex optimization. --- Delft University of Technology. --- Derivative. --- Differentiable function. --- Directional derivative. --- Division by zero. --- Dual space. --- Duality (mathematics). --- Duality gap. --- Eigenvalues and eigenvectors. --- Embedding. --- Equation. --- Estimation. --- Existential quantification. --- Explanation. --- Feasible region. --- Filter design. --- Function (mathematics). --- Implementation. --- Instance (computer science). --- Invertible matrix. --- Iteration. --- Jacobian matrix and determinant. --- Jordan algebra. --- Karmarkar's algorithm. --- Karush–Kuhn–Tucker conditions. --- Line search. --- Linear complementarity problem. --- Linear function. --- Linear programming. --- Lipschitz continuity. --- Local convergence. --- Loss function. --- Mathematician. --- Mathematics. --- Matrix function. --- McMaster University. --- Monograph. --- Multiplication operator. --- Newton's method. --- Nonlinear programming. --- Nonlinear system. --- Notation. --- Operations research. --- Optimal control. --- Optimization problem. --- Parameter (computer programming). --- Parameter. --- Pattern recognition. --- Polyhedron. --- Polynomial. --- Positive semidefinite. --- Positive-definite matrix. --- Quadratic function. --- Requirement. --- Result. --- Scientific notation. --- Second derivative. --- Self-concordant function. --- Sensitivity analysis. --- Sign (mathematics). --- Signal processing. --- Simplex algorithm. --- Simultaneous equations. --- Singular value. --- Smoothness. --- Solution set. --- Solver. --- Special case. --- Subset. --- Suggestion. --- Technical report. --- Theorem. --- Theory. --- Time complexity. --- Two-dimensional space. --- Upper and lower bounds. --- Variable (computer science). --- Variable (mathematics). --- Variational inequality. --- Variational principle. --- Without loss of generality. --- Worst-case complexity. --- Yurii Nesterov. --- Mathematical Optimization --- Mathematics --- Programming (mathematics)