Bilevel fractional programming; Farkas lemma; Farkas lemma: Generalizations; Fractional combinatorial optimization; Quadratic fractional programming: Dinkelbach methodBilevel fractional programming; Fractional combinatorial optimization; Quadratic fractional programming: Dinkelbach methodFRACTIONAL PROGRAMMING

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Hans Frenk | Siegfried Schaible

Fractional Programming

BOOK CHAPTER published 2008 in Encyclopedia of Optimization

Authors: Hans Frenk | Siegfried Schaible

Fractional Programming

BOOK CHAPTER published 2013 in Encyclopedia of Operations Research and Management Science

Authors: Siegfried Schaible

Fractional programming

BOOK CHAPTER published 2001 in Encyclopedia of Operations Research and Management Science

Authors: Siegfried Schaible

αBB algorithm; Concave programming; D.C. programming; Quadratic knapsack. Quadratic programming with bound constraints; Reverse convex optimization Standard quadratic optimization problems: Theory REVERSE CONVEX OPTIMIZATION

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Stephen E. Jacobsen

Multi-objective Fractional Programming Problems

BOOK CHAPTER published 2008 in Encyclopedia of Optimization

Authors: Zhian Liang

Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Integer linear complementary problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and bound methods; Integer programming: Branch and cut algorithms; Integer programming: Cutting plane algorithms; Integer programming duality; Lagrange, Joseph-Louis; Lagrangian multipliers methods for convex programming; LCP: Pardalos–Rosen mixed integer formulation; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multi-objective optimization: Lagrange duality; Multiparametric mixed integer linear programming; Parametric mixed integer nonlinear optimization; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem INTEGER PROGRAMMING: LAGRANGIAN RELAXATION

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: J. N. Hooker

Bilevel fractional programming; Combinatorial matrix analysis; Combinatorial optimization algorithms in resource allocation problem; Combinatorial optimization games; Complexity classes in optimization; Complexity of degeneracy; Complexity of gradients, Jacobians, and Hessians; Complexity theory; Complexity theory: Quadratic programming; Computational complexity theory; Evolutionary algorithms in combinatorial optimization; Fractional programming; Information-based complexity and information-based optimization; Kolmogorov complexity; Mixed integer nonlinear programming; Multi-objective combinatorial optimization; Neural networks for combinatorial optimization; NP-complete problems and proof methodology; Parallel computing: Complexity classes; Quadratic fractional programming: Dinkelbach method; Replicator dynamics in combinatorial optimizationBilevel fractional programming; Combinatorial matrix analysis; Combinatorial optimization algorithms in resource allocation problems; Combinatorial optimization games; Complexity classes in optimization; Complexity of degeneracy; Complexity of gradients, Jacobians, and Hessians; Complexity theory; Complexity theory: Quadratic programming; Computational complexity theory; Evolutionary algorithms in combinatorial optimization; Fractional programming; Information-based complexity and information-based optimization; Kolmogorov complexity; Mixed integer nonlinear programming; Multi-objective combinatorial optimization; NP-complete problems and proof methodology; Parallel computing: Complexity classes; Quadratic fractional programming: Dinkelbach method; Replicator dynamics in combinatorial optimization; Stochastic integer programsFRACTIONAL COMBINATORIAL OPTIMIZATION

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Tomasz Radzik

Inverse Problems and Computational Imaging

BOOK CHAPTER published 2005 in Encyclopedia of Modern Optics

Authors: M. Bertero | P. Boccacci

Branch and price: Integer programming with column generation; Convex-simplex algorithm; Decomposition techniques for MILP: Lagrangian relaxation; Equivalence between nonlinear complementarity problem and fixed point problem; Generalized nonlinear complementarity problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and bound methods; Integer programming: Branch and cut algorithms; Integer programming: Cutting plane algorithms; Integer programming duality; Integer programming: Lagrangian relaxation; LCP: Pardalos–Rosen mixed integer formulation; Lemke method; Linear complementarity problem; Linear programming; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multiparametric mixed integer linear programming; Order complementarity; Parametric linear programming: Cost simplex algorithm; Parametric mixed integer nonlinear optimization; Principal pivoting methods for linear complementarity problems; Sequential simplex method; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem; Topological methods in complementarity theory INTEGER LINEAR COMPLEMENTARY PROBLEM

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Panos M. Pardalos | Yasutoshi Yajima

Primal-Dual Linear-Programming Problems

BOOK CHAPTER published 2013 in Encyclopedia of Operations Research and Management Science

Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Integer linear complementary problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and bound methods; Integer programming: Branch and cut algorithms; Integer programming duality; Integer programming: Lagrangian relaxation; LCP: Pardalos–Rosen mixed integer formulation; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multiparametric mixed integer linear programming; NP-complete problems and proof methodology; Parametric mixed integer nonlinear optimization; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem INTEGER PROGRAMMING: CUTTING PLANE ALGORITHMS

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: John E. Mitchell

Duality for semidefinite programming; Entropy optimization: Interior point methods; Homogeneous selfdual methods for linear programming; Linear programming: Interior point methods; Linear programming: Karmarkar projective algorithm; Matrix completion problems; Potential reduction methods for linear programming; Semi-infinite programming, semidefinite programming and perfect duality; Semidefinite programming and determinant maximization; Semidefinite programming and structural optimization; Semidefinite programming: Optimality conditions and stability; Sequential quadratic programming: Interior point methods for distributed optimal control problems; Solving large scale and sparse semidefinite programs; Successive quadratic programming: Solution by active sets and interior point methods INTERIOR POINT METHODS FOR SEMIDEFINITE PROGRAMMING

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Levent Tunç

Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Integer linear complementary problem; Integer programming; Integer programming: Branch and bound methods; Integer programming: Branch and cut algorithms; Integer programming: Cutting plane algorithms; Integer programming duality; Integer programming: Lagrangian relaxation: LCP: Pardalos–Rosen mixed integer formulation; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multiparametric mixed integer linear programming; Parametric mixed integer nonlinear optimization; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem INTEGER PROGRAMMING: ALGEBRAIC METHODS

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Rekha R. Thomas

Airline optimization; Alignment problem; Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Graph coloring; Integer linear complementary problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and bound methods; Integer programming: Branch and cut algorithms; Integer programming: Cutting plane algorithms; Integer programming duality; Integer programming: Lagrangian relaxation; LCP: Pardalos–Rosen mixed integer formulation; Maximum satisfiability problem; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multidimensional knapsack problems; Multiparametric mixed integer linear programming; Optimization in leveled graphs; Parametric mixed integer nonlinear optimization; Quadratic knapsack; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming: Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem; Vehicle scheduling INTEGER PROGRAMMING

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Egon Balas

Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Integer linear complementary problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and bound methods; Integer programming: Cutting plane algorithms; Integer programming duality; Integer programming: Lagrangian relaxation; LCP: Pardalos–Rosen mixed integer formulation; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multiparametric mixed integer linear programming; Parametric mixed integer nonlinear optimization; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem INTEGER PROGRAMMING: BRANCH AND CUT ALGORITHMS

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: John E. Mitchell

Primal-dual Linear-programming problems

BOOK CHAPTER published 2001 in Encyclopedia of Operations Research and Management Science

Authors: Saul I. Gass | Carl M. Harris

Branch and price: Integer programming with column generation; Decomposition techniques for MILP: Lagrangian relaxation; Genetic algorithms; Integer linear complementary problem; Integer programming; Integer programming: Algebraic methods; Integer programming: Branch and cut algorithms; Integer programming: Cutting plane algorithms; Integer programming duality; Integer programming: Lagrangian relaxation; LCP: Pardalos–Rosen mixed integer formulation, Linear programming; Interior point methods; Mixed integer classification problems; Multi-objective integer linear programming; Multi-objective mixed integer programming; Multiparametric mixed integer linear programming; Parametric mixed integer nonlinear optimization; Set covering, packing and partitioning problems; Simplicial pivoting algorithms for integer programming; Stochastic integer programming: Continuity, stability, rates of convergence; Stochastic integer programs; Time-dependent traveling salesman problem INTEGER PROGRAMMING: BRANCH AND BOUND METHODS

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Eva K. Lee | John E. Mitchell

Complexity classes in optimization; Complexity of degeneracy; Complexity of gradients, Jacobians, and Hessians; Complexity theory; Complexity theory: Quadratic programming; Computational complexity theory; Fractional combinatorial optimization; Kolmogorov complexity; Mixed integer nonlinear programming; NP-complete problems and proof methodology; Parallel computing: Complexity classes INFORMATION-BASED COMPLEXITY AND INFORMATION-BASED OPTIMIZATION

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: J. F. Traub | A. G. Werschulz

αBB algorithm; Eigenvalue enclosures for ordinary differential equations; Generalized monotonicity: Applications to variational inequalities and equilibrium problems; Hemivariational inequalities: Applications in mechanics; Hemivariational inequalities: Static problems; Interval analysis: Eigenvalue bounds of interval matrices; Non-convex energy functions: Hemivariational inequalities; Nonconvex-nonsmooth calculus of variations; Quasidifferentiable optimization; Quasidifferentiable optimization: Algorithms for hypodifferentiable functions; Quasidifferentiable optimization: Algorithms for QD functions; Quasidifferentiable optimization: Applications; Quasidifferentiable optimization: Applications to thermoelasticity; Quasidifferentiable optimization: Calculus of quasidifferentials; Quasidifferentiable optimization: Codifferentiable functions; Quasidifferentiable optimization: Dini derivatives, Clarke derivatives; Quasidifferentiable optimization: Exact penalty methods; Quasidifferentiable optimization: Optimality conditions; Quasidifferentiable optimization: Stability of dynamic systems; Quasidifferentiable optimization: Variational formulations; Quasivariational inequalities; Semidefinite programming and determinant maximization; Sensitivity analysis of variational inequality problems; Solving hemivariational inequalities by nonsmooth optimization methods; Variational inequalities; Variational inequalities: F. E. approach; Variational inequalities: Geometric interpretation, existence and uniqueness; Variational inequalities: Projected dynamical system; Variational principles HEMIVARIATIONAL INEQUALITIES: EIGENVALUE PROBLEMS

BOOK CHAPTER published 2001 in Encyclopedia of Optimization

Authors: Daniel Goeleven | Dumitru Motreanu