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Mathematical optimization --- Algorithms --- Algorism --- Mathematical Sciences --- Applied Mathematics --- Algebra --- Arithmetic --- Foundations --- Algorithms. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis

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Functional analysis --- Differential equations, Hyperbolic. --- Calculus of variations. --- Mathematical physics --- 51 --- Boundary value problems --- Calculus of variations --- Differential equations, Hyperbolic --- Physical mathematics --- Physics --- Functional calculus --- Functional equations --- Integral equations --- Hyperbolic differential equations --- Differential equations, Partial --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Initial value problems --- Mathematics --- 51 Mathematics

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Operational research. Game theory --- Network analysis (Planning) --- Mathematical optimization --- Algorithms --- Analyse de réseau (Planification) --- Optimisation mathématique --- Algorithmes --- 519.85 --- Project networks --- Planning --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Algorism --- Algebra --- Arithmetic --- Mathematical programming --- Foundations --- Algorithms. --- Mathematical optimization. --- Network analysis (Planning). --- 519.85 Mathematical programming --- Analyse de réseau (Planification) --- Optimisation mathématique

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Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.

Lineaire programmering --- Linear programming --- Programmation (Mathematiques) --- Programmation lineaire --- Programmeren (Wiskunde) --- Programming (Mathematics) --- #TELE:SISTA --- 681.3*G16 --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Linear programming. --- Mathematics. --- Numerical analysis. --- Systems theory. --- Mathematical optimization. --- Applications of Mathematics. --- Numerical Analysis. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science

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Numerical solutions of algebraic equations --- Numerical methods of optimisation --- Algebras, Linear. --- Numerical calculations. --- Mathematical optimization. --- 519.66 --- Algebras, Linear --- Mathematical optimization --- Numerical calculations --- #KVIV:BB --- 512.64 --- 519.6 --- 519.85 --- 681.3*G16 --- Numerical analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Calculus of operations --- Line geometry --- Topology --- Mathematic tables and their compilation --- Linear and multilinear algebra. Matrix theory --- Computational mathematics. Numerical analysis. Computer programming --- Mathematical programming --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.85 Mathematical programming --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 512.64 Linear and multilinear algebra. Matrix theory --- 519.66 Mathematic tables and their compilation --- lineaire algebra --- Programmation (mathématiques) --- Algebre lineaire --- Methodes numeriques