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2022 Wirtschaftswissenschaften Oliver Stein

Mixed-Integer Optimization II, Section 3.4 (Generalized Benders decomposition, Introduction)

Mixed-Integer Optimization II, Section 3.4 (Generalized Benders decomposition, Introduction)

Oliver Stein

Mixed-Integer Optimization II, Section 3.7.1 (Dantzig-Wolfe decomposition, motivation and construction)

Mixed-Integer Optimization II, Section 3.7.1 (Dantzig-Wolfe decomposition, motivation and construction)

Oliver Stein

Mixed-Integer Optimization II, Section 3.6.4 (A subgradient method)

Mixed-Integer Optimization II, Section 3.6.4 (A subgradient method)

Oliver Stein

Mixed-Integer Optimization II, Section 3.6.1 (Lagrange relaxation, construction and relaxation property)

Mixed-Integer Optimization II, Section 3.6.1 (Lagrange relaxation, construction and relaxation property)

Oliver Stein

Mixed-Integer Optimization II, Section 3.5.4 (Cutting plane method for MICP), part 2

Mixed-Integer Optimization II, Section 3.5.4 (Cutting plane method for MICP), part 2

Oliver Stein

Mixed-Integer Optimization II, Section 3.5.3 (Optimality cuts)

Mixed-Integer Optimization II, Section 3.5.3 (Optimality cuts)

Oliver Stein

Mixed-Integer Optimization II, Section 3.5.2 (Feasibility cuts)

Mixed-Integer Optimization II, Section 3.5.2 (Feasibility cuts)

Oliver Stein

Mixed-Integer Optimization II, Section 3.8.3 (Feasibility pump), Section 3.8.4 (Metaheuristics)

Mixed-Integer Optimization II, Section 3.8.3 (Feasibility pump), Section 3.8.4 (Metaheuristics)

Oliver Stein

Mixed-Integer Optimization II, Section 3.7.3 (Pricing)

Mixed-Integer Optimization II, Section 3.7.3 (Pricing)

Oliver Stein

Mixed-Integer Optimization II, Section 3.8.1 (Diving heuristics), Section 3.8.2 (Local branching)

Mixed-Integer Optimization II, Section 3.8.1 (Diving heuristics), Section 3.8.2 (Local branching)

Oliver Stein

Mixed-Integer Optimization II, Section 3.7.4 (Initialization)

Mixed-Integer Optimization II, Section 3.7.4 (Initialization)

Oliver Stein

Mixed-Integer Optimization II, Section 3.7.2 (Column generation)

Mixed-Integer Optimization II, Section 3.7.2 (Column generation)

Oliver Stein

Mixed-Integer Optimization II, Section 3.6.3 (Comparison to continuous relaxation)

Mixed-Integer Optimization II, Section 3.6.3 (Comparison to continuous relaxation)

Oliver Stein

Mixed-Integer Optimization II, Section 3.6.2 (Decomposition by Lagrange relaxation)

Mixed-Integer Optimization II, Section 3.6.2 (Decomposition by Lagrange relaxation)

Oliver Stein

Mixed-Integer Optimization II, Section 3.5.4 (Cutting plane method for MICP), part 1

Mixed-Integer Optimization II, Section 3.5.4 (Cutting plane method for MICP), part 1

Oliver Stein

Mixed-Integer Optimization II, Section 3.5.1 (Motivation of the Outer Approximation method)

Mixed-Integer Optimization II, Section 3.5.1 (Motivation of the Outer Approximation method)

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.7 (Cutting plane method for MICP), part 2

Mixed-Integer Optimization II, Section 3.4.7 (Cutting plane method for MICP), part 2

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.7 (Cutting plane method for MICP), part 1

Mixed-Integer Optimization II, Section 3.4.7 (Cutting plane method for MICP), part 1

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.6 (Feasibility cuts)

Mixed-Integer Optimization II, Section 3.4.6 (Feasibility cuts)

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 3

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 3

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 2

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 2

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.3 (A functional description of the reduced feasible set)

Mixed-Integer Optimization II, Section 3.4.3 (A functional description of the reduced feasible set)

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.4 (A purely discrete problem equivalent to MICP)

Mixed-Integer Optimization II, Section 3.4.4 (A purely discrete problem equivalent to MICP)

Oliver Stein

Mixed-Integer Optimization II, Section 3.2 (Continuous relaxation and rounding)

Mixed-Integer Optimization II, Section 3.2 (Continuous relaxation and rounding)

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 1

Mixed-Integer Optimization II, Section 3.4.5 (Optimality cuts), part 1

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.1 (Reduced feasible set and reduced objective function)

Mixed-Integer Optimization II, Section 3.4.1 (Reduced feasible set and reduced objective function)

Oliver Stein

Mixed-Integer Optimization II, Section 3.4.2 (Convexity of the reduced feasible set and of the reduced objective function)

Mixed-Integer Optimization II, Section 3.4.2 (Convexity of the reduced feasible set and of the reduced objective function)

Oliver Stein

Mixed-Integer Optimization II, Section 3.3.1 (B&B für MINLP - A conceptual algorithm), Section 3.3.2 (The convex case)

Mixed-Integer Optimization II, Section 3.3.1 (B&B für MINLP - A conceptual algorithm), Section 3.3.2 (The convex case)

Oliver Stein

Mixed-Integer Optimization II, Section 3.3.3 (The nonconvex case)

Mixed-Integer Optimization II, Section 3.3.3 (The nonconvex case)

Oliver Stein

Mixed-Integer Optimization II, Section 3.1 (Models in portfolio optimization)

Mixed-Integer Optimization II, Section 3.1 (Models in portfolio optimization)

Oliver Stein

Mixed-Integer Optimization II, Section 3 (Mixed-integer nonlinear optimization), Introduction

Mixed-Integer Optimization II, Section 3 (Mixed-integer nonlinear optimization), Introduction

Oliver Stein

Parametric Optimization, Section 2.3.7 (Sensitivity of nondegenerate minimal values), part 2

Parametric Optimization, Section 2.3.7 (Sensitivity of nondegenerate minimal values), part 2

Oliver Stein

Parametric Optimization, Section 2.3.5 (Stability of nondegenerate minimal points)

Parametric Optimization, Section 2.3.5 (Stability of nondegenerate minimal points)

Oliver Stein

Parametric Optimization, Section 2.3.7 (Sensitivity of nondegenerate minimal values), part 1

Parametric Optimization, Section 2.3.7 (Sensitivity of nondegenerate minimal values), part 1

Oliver Stein

Parametric Optimization, Section 2.3.2 (Three regularity conditions)

Parametric Optimization, Section 2.3.2 (Three regularity conditions)

Oliver Stein

Parametric Optimization, Section 2.3.1 (Criticality notions for constrained problems)

Parametric Optimization, Section 2.3.1 (Criticality notions for constrained problems)

Oliver Stein

Parametric Optimization, Section 4.1.3 (Optimality conditions)

Parametric Optimization, Section 4.1.3 (Optimality conditions)

Oliver Stein

Parametric Optimization

Parametric Optimization

Oliver Stein

Parametric Optimization, Section 3.2.2 (Applications and characterizations for semicontinuity properties of functions)

Parametric Optimization, Section 3.2.2 (Applications and characterizations for semicontinuity properties of functions)

Oliver Stein

Parametric Optimization, Section 4.1.4 (Reduction Ansatz)

Parametric Optimization, Section 4.1.4 (Reduction Ansatz)

Oliver Stein

Parametric Optimization, Section 3.7 (Directional sensitivity of minimal values)

Parametric Optimization, Section 3.7 (Directional sensitivity of minimal values)

Oliver Stein

Parametric Optimization, Section 2.2.3 (Quadratic indices), Section 2.2.4 (Stability of nondegenerate minimal points)

Parametric Optimization, Section 2.2.3 (Quadratic indices), Section 2.2.4 (Stability of nondegenerate minimal points)

Oliver Stein

Parametric Optimization, Section 1.9 (Counter examples)

Parametric Optimization, Section 1.9 (Counter examples)

Oliver Stein

Parametric Optimization, Section 1.3 (Algorithms and a fourth key question), Section 1.4 (Decomposition methods), Section 1.5 (Robust and semi-infinite optimization)

Parametric Optimization, Section 1.3 (Algorithms and a fourth key question), Section 1.4 (Decomposition methods), Section 1.5 (Robust and semi-infinite optimization)

Oliver Stein

Parametric Optimization, Section 1.1 (Shadow prices and three key questions), Section 1.2 (Hotelling's lemma and the same questions)

Parametric Optimization, Section 1.1 (Shadow prices and three key questions), Section 1.2 (Hotelling's lemma and the same questions)

Oliver Stein

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 3

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 3

Oliver Stein

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 2

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 2

Oliver Stein

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 1

Global Optimization I, Section 2.8.5 (Frank-Wolfe method), part 1

Oliver Stein

Global Optimization I, Section 2.8.4 (Kelley's cutting plane method), part 1

Global Optimization I, Section 2.8.4 (Kelley's cutting plane method), part 1

Oliver Stein

Global Optimization I, Section 2.8.4 (Kelley's cutting plane method), part 2

Global Optimization I, Section 2.8.4 (Kelley's cutting plane method), part 2

Oliver Stein

Global Optimization I, Section 2.8 (Numerical methods); Section 2.8.1 (Basic idea of the gradient method)

Global Optimization I, Section 2.8 (Numerical methods); Section 2.8.1 (Basic idea of the gradient method)

Oliver Stein

Global Optimization I, Section 2.7.2 (The KKT conditions)

Global Optimization I, Section 2.7.2 (The KKT conditions)

Oliver Stein

Global Optimization I, Section 2.7.1 (Lagrange- and Wolfe-duality), part 3

Global Optimization I, Section 2.7.1 (Lagrange- and Wolfe-duality), part 3

Oliver Stein

Global Optimization I, Section 2.7.1 (Lagrange- and Wolfe-duality), part 2

Global Optimization I, Section 2.7.1 (Lagrange- and Wolfe-duality), part 2

Oliver Stein

Global Optimization I, Section 2.2.1 (Higher-dimensional first derivatives)

Global Optimization I, Section 2.2.1 (Higher-dimensional first derivatives)

Oliver Stein

Global Optimization I, Section 2.1 (Convexity), part 2

Global Optimization I, Section 2.1 (Convexity), part 2

Oliver Stein

Global Optimization I, Section 1.2.4 (Unbounded feasible sets), part 2

Global Optimization I, Section 1.2.4 (Unbounded feasible sets), part 2

Oliver Stein

Global Optimization I, Section 1.2.1 (Definition of solvability)

Global Optimization I, Section 1.2.1 (Definition of solvability)

Oliver Stein

Parametric Optimization, Section 3.3.2 (Closedness and local boundedness of unconstrained minimal points)

Parametric Optimization, Section 3.3.2 (Closedness and local boundedness of unconstrained minimal points)

Oliver Stein

Parametric Optimization, Section 3.3.1 (Basic concepts for setvalued mappings)

Parametric Optimization, Section 3.3.1 (Basic concepts for setvalued mappings)

Oliver Stein

Parametric Optimization, Section 3.2.5 (Continuity of unconstrained minimal values)

Parametric Optimization, Section 3.2.5 (Continuity of unconstrained minimal values)

Oliver Stein

Parametric Optimization, Section 3.2.4 (Lower semicontinuity of unconstrained minimal values), part 1

Parametric Optimization, Section 3.2.4 (Lower semicontinuity of unconstrained minimal values), part 1

Oliver Stein

Parametric Optimization, Section 3.2.4 (Lower semicontinuity of minimal values), part 3

Parametric Optimization, Section 3.2.4 (Lower semicontinuity of minimal values), part 3

Oliver Stein

Parametric Optimization, Section 3.2.3 (Upper semicontinuity of unconstrained minimal values)

Parametric Optimization, Section 3.2.3 (Upper semicontinuity of unconstrained minimal values)

Oliver Stein

Parametric Optimization, Section 3.2.1 (Semicontinuity of functions)

Parametric Optimization, Section 3.2.1 (Semicontinuity of functions)

Oliver Stein

Parametric Optimization, Section 3.1 (Preliminary thoughts)

Parametric Optimization, Section 3.1 (Preliminary thoughts)

Oliver Stein

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 3

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 3

Oliver Stein

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 2

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 2

Oliver Stein

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 1

Global Optimization I, Section 2.8.6 (Basic idea of primal-dual IPMs), part 1

Oliver Stein

Global Optimization I, Section 2.8.3 (Basic idea of cutting plane methods)

Global Optimization I, Section 2.8.3 (Basic idea of cutting plane methods)

Oliver Stein

Global Optimization I, Section 2.8.2 (Basic idea of Newton's method)

Global Optimization I, Section 2.8.2 (Basic idea of Newton's method)

Oliver Stein

Parametric Optimization, Section 2.2.1 (Preliminary thoughts)

Parametric Optimization, Section 2.2.1 (Preliminary thoughts)

Oliver Stein

Parametric Optimization, Section 2.1 (Basic terminology and notation)

Parametric Optimization, Section 2.1 (Basic terminology and notation)

Oliver Stein

Parametric Optimization, Section 1.6 (Bilevel optimization), Section 1.7 (Nash games), Section 1.8 (Multiobjective optimization)

Parametric Optimization, Section 1.6 (Bilevel optimization), Section 1.7 (Nash games), Section 1.8 (Multiobjective optimization)

Oliver Stein

Parametric Optimization, Section 2.3.3 (Nondegenerate critical points), Section 2.3.4 (Linear and quadratic indices)

Parametric Optimization, Section 2.3.3 (Nondegenerate critical points), Section 2.3.4 (Linear and quadratic indices)

Oliver Stein

Parametric Optimization, Section 2.3.6 (Sensitivity of nondegenerate minimal points)

Parametric Optimization, Section 2.3.6 (Sensitivity of nondegenerate minimal points)

Oliver Stein

Parametric Optimization, Section 2.2.6 (Sensitivity of nondegenerate minimal values)

Parametric Optimization, Section 2.2.6 (Sensitivity of nondegenerate minimal values)

Oliver Stein

Parametric Optimization, Section 2.2.5 (Sensitivity of nondegenerate minimal points)

Parametric Optimization, Section 2.2.5 (Sensitivity of nondegenerate minimal points)

Oliver Stein

Parametric Optimization, Section 2.2.2 (Nondegenerate critical points)

Parametric Optimization, Section 2.2.2 (Nondegenerate critical points)

Oliver Stein

Global Optimization I, Section 2.7.5 (Constraint Qualifications)

Global Optimization I, Section 2.7.5 (Constraint Qualifications)

Oliver Stein

Global Optimization I, Section 2.7.4 (Geometric interpretation of the KKT conditions)

Global Optimization I, Section 2.7.4 (Geometric interpretation of the KKT conditions)

Oliver Stein

Global Optimization I, Section 2.7.3 (Complementarity)

Global Optimization I, Section 2.7.3 (Complementarity)

Oliver Stein

Global Optimization I, Section 2.7 (Optimality conditions for constrained convex problems); Section 2.7.1 (Lagrange- and Wolfe-duality), part 1

Global Optimization I, Section 2.7 (Optimality conditions for constrained convex problems); Section 2.7.1 (Lagrange- and Wolfe-duality), part 1

Oliver Stein

Global Optimization I, Section 2.6 (Monotonicity characterization of convexity)

Global Optimization I, Section 2.6 (Monotonicity characterization of convexity)

Oliver Stein

Global Optimization I, Section 2.5.2 (C2-characterizations)

Global Optimization I, Section 2.5.2 (C2-characterizations)

Oliver Stein

Global Optimization I, Section 2.5.1 (Higher-dimensional second derivatives)

Global Optimization I, Section 2.5.1 (Higher-dimensional second derivatives)

Oliver Stein

Global Optimization I, Section 2.4 (Optimality conditions for unconstrained convex problems)

Global Optimization I, Section 2.4 (Optimality conditions for unconstrained convex problems)

Oliver Stein

Mixed-Integer Optimization I, Section 2 (Mixed-integer linear optimization), Introduction

Mixed-Integer Optimization I, Section 2 (Mixed-integer linear optimization), Introduction

Oliver Stein

Parametric Optimization, Section 4.2.4 (An equivalent optimization problem), Section 4.2.5 (Regularization of the gap function), Section 4.2.6 (Continuity of the gap fct.), Section 4.2.7 (Differentiability of the gap fct.)

Parametric Optimization, Section 4.2.4 (An equivalent optimization problem), Section 4.2.5 (Regularization of the gap function), Section 4.2.6 (Continuity of the gap fct.), Section 4.2.7 (Differentiability of the gap fct.)

Oliver Stein

Parametric Optimization, Section 4.2.2 (The combined KKT system)

Parametric Optimization, Section 4.2.2 (The combined KKT system)

Oliver Stein

Parametric Optimization, Section 4.2.1 (Nash game definitions and examples)

Parametric Optimization, Section 4.2.1 (Nash game definitions and examples)

Oliver Stein

Mixed-Integer Optimization I, Section 2.2 (Solvability)

Mixed-Integer Optimization I, Section 2.2 (Solvability)

Oliver Stein

Mixed-Integer Optimization I, Section 2.5.2 (The purely integer case), part 1

Mixed-Integer Optimization I, Section 2.5.2 (The purely integer case), part 1

Oliver Stein

Parametric Optimization, Section 4.1.2 (Topological properties of the feasible set)

Parametric Optimization, Section 4.1.2 (Topological properties of the feasible set)

Oliver Stein

Parametric Optimization, Section 4.1.1 (SIP examples)

Parametric Optimization, Section 4.1.1 (SIP examples)

Oliver Stein

Parametric Optimization, Section 3.5 (Continuity properties of constrained minimal values), Section 3.6 (Continuity properties of constrained minimal points)

Parametric Optimization, Section 3.5 (Continuity properties of constrained minimal values), Section 3.6 (Continuity properties of constrained minimal points)

Oliver Stein

Parametric Optimization, Section 3.4 (Continuity properties of the feasible set mapping)

Parametric Optimization, Section 3.4 (Continuity properties of the feasible set mapping)

Oliver Stein

Parametric Optimization, Section 3.3.3 (Semicontinuity properties of setvalued mappings)

Parametric Optimization, Section 3.3.3 (Semicontinuity properties of setvalued mappings)

Oliver Stein

Global Optimization I, Section 1.2.3 (Weierstrass theorem)

Global Optimization I, Section 1.2.3 (Weierstrass theorem)

Oliver Stein

Global Optimization I, Section 1.1 (Examples and notions), part 3

Global Optimization I, Section 1.1 (Examples and notions), part 3

Oliver Stein

Global Optimization I, Section 1.1 (Examples and notions), part 2

Global Optimization I, Section 1.1 (Examples and notions), part 2

Oliver Stein

Global Optimization I, Section 1.1 (Examples and notions), part 1

Global Optimization I, Section 1.1 (Examples and notions), part 1

Oliver Stein

Parametric Optimization, Introduction

Parametric Optimization, Introduction

Oliver Stein

Global Optimization I, Section 2.3 (Solvability of convex optimization problems)

Global Optimization I, Section 2.3 (Solvability of convex optimization problems)

Oliver Stein

Global Optimization I, Section 2.2.2 (C1-characterization)

Global Optimization I, Section 2.2.2 (C1-characterization)

Oliver Stein

Global Optimization I, Section 2.1 (Convexity), part 1

Global Optimization I, Section 2.1 (Convexity), part 1

Oliver Stein

Global Optimization I, Section 1.2.5 (Non-closed feasible sets)

Global Optimization I, Section 1.2.5 (Non-closed feasible sets)

Oliver Stein

Global Optimization I, Section 1.2.4 (Unbounded feasible sets), part 1

Global Optimization I, Section 1.2.4 (Unbounded feasible sets), part 1

Oliver Stein

Global Optimization I, Section 1.2.2 (Types of unsolvability)

Global Optimization I, Section 1.2.2 (Types of unsolvability)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.10 (Iterative solution by a cutting plane method), part 2

Mixed-Integer Optimization I, Section 2.6.10 (Iterative solution by a cutting plane method), part 2

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.7 (A dual description of the reduced feasible set)

Mixed-Integer Optimization I, Section 2.6.7 (A dual description of the reduced feasible set)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.8 (The Benders reformulation of MILP)

Mixed-Integer Optimization I, Section 2.6.8 (The Benders reformulation of MILP)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.6 (A dual description of the reduced objective function)

Mixed-Integer Optimization I, Section 2.6.6 (A dual description of the reduced objective function)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.5 (A purely discrete problem, equivalent to MILP)

Mixed-Integer Optimization I, Section 2.6.5 (A purely discrete problem, equivalent to MILP)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.4 (Unsolvability and connections between the inner problems)

Mixed-Integer Optimization I, Section 2.6.4 (Unsolvability and connections between the inner problems)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.3 (A functional description of the reduced feasible set)

Mixed-Integer Optimization I, Section 2.6.3 (A functional description of the reduced feasible set)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.2 (The reduced objective function of MILP)

Mixed-Integer Optimization I, Section 2.6.2 (The reduced objective function of MILP)

Oliver Stein

Mixed-Integer Optimization I, Section 2.6.1 (Benders decomposition / general decomposition)

Mixed-Integer Optimization I, Section 2.6.1 (Benders decomposition / general decomposition)

Oliver Stein

Global Optimization II, Section 3.9.3 (A variation of Alg. 3.5)

Global Optimization II, Section 3.9.3 (A variation of Alg. 3.5)

Oliver Stein

Global Optimization II, Section 3.9.1 (Properties of Lipschitz continuous functions), part 2

Global Optimization II, Section 3.9.1 (Properties of Lipschitz continuous functions), part 2

Oliver Stein