IEEE Transactions on Power Systems, ISSN 0885-8950, 05/2018, Volume 33, Issue 3, pp. 2906 - 2918

.... We then discuss different chance-constraint reformulations and solution approaches for the problem...

Reactive power | Uncertainty | reformulation methods | AC optimal power flow | solution algorithms | chance constraints | Mathematical model | Iterative methods | Voltage control | Optimization | UNIT COMMITMENT | NETWORK | UNCERTAINTIES | SCENARIO APPROACH | OPERATIONS | ROBUST OPTIMIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | SECURITY | GENERATION | Flow equations | Constraints | Iterative solution | Mathematical analysis | Power flow | MATHEMATICS AND COMPUTING | Mathematics | POWER TRANSMISSION AND DISTRIBUTION

Reactive power | Uncertainty | reformulation methods | AC optimal power flow | solution algorithms | chance constraints | Mathematical model | Iterative methods | Voltage control | Optimization | UNIT COMMITMENT | NETWORK | UNCERTAINTIES | SCENARIO APPROACH | OPERATIONS | ROBUST OPTIMIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | SECURITY | GENERATION | Flow equations | Constraints | Iterative solution | Mathematical analysis | Power flow | MATHEMATICS AND COMPUTING | Mathematics | POWER TRANSMISSION AND DISTRIBUTION

Journal Article

Mathematical programming, ISSN 1436-4646, 2017, Volume 171, Issue 1-2, pp. 115 - 166

... the Wasserstein metric: performance guarantees and tractable reformulations Peyman Mohajerin Esfahani1 Â· Daniel Kuhn2 Received: 9 May 2015 / Accepted: 16 June 2017...

90C25 Convex programming | 90C47 Minimax problems | Mathematical Methods in Physics | 90C15 Stochastic programming | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PORTFOLIO OPTIMIZATION | MATHEMATICS, APPLIED | DISTANCE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RISK MEASURES | INEQUALITIES | MODELS | COUNTERPARTS | AMBIGUITY | CONVEX-OPTIMIZATION | Training | Economic models | Global optimization | Parameter uncertainty | Optimization techniques | Nonlinear programming | Monte Carlo simulation

90C25 Convex programming | 90C47 Minimax problems | Mathematical Methods in Physics | 90C15 Stochastic programming | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | PORTFOLIO OPTIMIZATION | MATHEMATICS, APPLIED | DISTANCE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RISK MEASURES | INEQUALITIES | MODELS | COUNTERPARTS | AMBIGUITY | CONVEX-OPTIMIZATION | Training | Economic models | Global optimization | Parameter uncertainty | Optimization techniques | Nonlinear programming | Monte Carlo simulation

Journal Article

Industrial & Engineering Chemistry Research, ISSN 0888-5885, 08/2018, Volume 57, Issue 30, pp. 9915 - 9924

.... To develop a model suitable for optimization, reformulation steps consisting of function smoothening, reducing model size, and scaling are applied to a predictive energy-based model for mAb...

ANIMAL-CELLS | ENGINEERING, CHEMICAL | SINGLE | PROTEIN | METABOLISM | GROWTH | FED-BATCH CULTIVATION | MEDIUM DESIGN | GLYCOSYLATION | MAMMALIAN-CELLS | CULTURE

ANIMAL-CELLS | ENGINEERING, CHEMICAL | SINGLE | PROTEIN | METABOLISM | GROWTH | FED-BATCH CULTIVATION | MEDIUM DESIGN | GLYCOSYLATION | MAMMALIAN-CELLS | CULTURE

Journal Article

Mathematical programming, ISSN 1436-4646, 2016, Volume 162, Issue 1-2, pp. 115 - 144

...Math. Program., Ser. A (2017) 162:115â€“144 DOI 10.1007/s10107-016-1032-4 FULL LENGTH PAPER Quadratic reformulations of nonlinear binary optimization problems...

Theoretical, Mathematical and Computational Physics | Pseudo-Boolean functions | Mathematics | Quadratic binary optimization | 90C09 | 90C20 | 90C10 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Reformulation methods | Combinatorics | Nonlinear binary optimization | MATHEMATICS, APPLIED | GRAPH CUTS | GENERALIZED ROOF DUALITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENERGY MINIMIZATION | QUBO | UNIONS | LOCAL SEARCH HEURISTICS | Machine vision | Studies | Optimization algorithms | Binary system | Upper bounds | Mathematical analysis | Nonlinearity | Mathematical models | Polynomials | Arrays | Cost engineering | Optimization

Theoretical, Mathematical and Computational Physics | Pseudo-Boolean functions | Mathematics | Quadratic binary optimization | 90C09 | 90C20 | 90C10 | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Reformulation methods | Combinatorics | Nonlinear binary optimization | MATHEMATICS, APPLIED | GRAPH CUTS | GENERALIZED ROOF DUALITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ENERGY MINIMIZATION | QUBO | UNIONS | LOCAL SEARCH HEURISTICS | Machine vision | Studies | Optimization algorithms | Binary system | Upper bounds | Mathematical analysis | Nonlinearity | Mathematical models | Polynomials | Arrays | Cost engineering | Optimization

Journal Article

Computers & chemical engineering, ISSN 0098-1354, 2019, Volume 125, pp. 89 - 97

The Duran-Grossmann model can deal with heat integration problems with variable process streams. Work and Heat Exchange Networks (WHENs) represent an extension...

MINLP | Duran-Grossmann model | disjunctive programming | Work and heat exchange networks | Reformulations | DESIGN | EXERGY | PROCESS OPTIMIZATION | PINCH ANALYSIS | ENGINEERING, CHEMICAL | COST | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION

MINLP | Duran-Grossmann model | disjunctive programming | Work and heat exchange networks | Reformulations | DESIGN | EXERGY | PROCESS OPTIMIZATION | PINCH ANALYSIS | ENGINEERING, CHEMICAL | COST | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION

Journal Article

6.
Full Text
Quadratic convex reformulation for quadratic programming with linear onâ€“off constraints

European journal of operational research, ISSN 0377-2217, 2019, Volume 274, Issue 3, pp. 824 - 836

â€˘Advance the state-of-the-art for quadratic programming with onâ€“off constraints.â€˘Generalize the quadratic convex reformulation approach...

Integer programming | Mixed integer quadratic programming | Semidefinite program | Quadratic convex reformulation | Onâ€“off constraint | On-off constraint | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Quadratic programming | Usage

Integer programming | Mixed integer quadratic programming | Semidefinite program | Quadratic convex reformulation | Onâ€“off constraint | On-off constraint | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Quadratic programming | Usage

Journal Article

7.
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Solving global optimization problems using reformulations and signomial transformations

Computers and Chemical Engineering, ISSN 0098-1354, 08/2018, Volume 116, pp. 122 - 134

....â€˘Lifting transformation schemes based on power, exponential and Î±BB-type reformulations is used...

Global optimization | Twice-differentiable nonconvex functions | Reformulation techniques | Signomial functions | Î± reformulation | Power transformations | Difference of convex functions | Exponential transformations | Î±BB convex underestimator | Nonconvex MINLP | MONOMIALS | ENGINEERING, CHEMICAL | ALPHA-BB | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENVELOPES | FRAMEWORK | alpha BB convex underestimator | alpha reformulation | CONVEX UNDERESTIMATION | Usage | Algorithms

Global optimization | Twice-differentiable nonconvex functions | Reformulation techniques | Signomial functions | Î± reformulation | Power transformations | Difference of convex functions | Exponential transformations | Î±BB convex underestimator | Nonconvex MINLP | MONOMIALS | ENGINEERING, CHEMICAL | ALPHA-BB | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENVELOPES | FRAMEWORK | alpha BB convex underestimator | alpha reformulation | CONVEX UNDERESTIMATION | Usage | Algorithms

Journal Article

Mathematical programming, ISSN 1436-4646, 2014, Volume 149, Issue 1-2, pp. 391 - 424

Dantzigâ€“Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs...

Matrix re-ordering | 65K05 | Theoretical, Mathematical and Computational Physics | Block-diagonal matrix | Automatic reformulation | Mathematics | Mathematical Methods in Physics | Column generation | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Dantzigâ€“Wolfe decomposition | Hypergraph partitioning | Numerical Analysis | 90C11 | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | DECOMPOSITION | LIBRARY | Dantzig-Wolfe decomposition | Management science | Integer programming | Studies | Analysis | Mixed integer | Construction | State of the art | Communities | Mathematical analysis | Solvers | Tools | Decomposition | Estimates

Matrix re-ordering | 65K05 | Theoretical, Mathematical and Computational Physics | Block-diagonal matrix | Automatic reformulation | Mathematics | Mathematical Methods in Physics | Column generation | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Dantzigâ€“Wolfe decomposition | Hypergraph partitioning | Numerical Analysis | 90C11 | 49M27 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATRICES | DECOMPOSITION | LIBRARY | Dantzig-Wolfe decomposition | Management science | Integer programming | Studies | Analysis | Mixed integer | Construction | State of the art | Communities | Mathematical analysis | Solvers | Tools | Decomposition | Estimates

Journal Article

Mathematical programming, ISSN 1436-4646, 2012, Volume 138, Issue 1-2, pp. 447 - 473

We consider the bilevel programming problem and its optimal value and KKT one level reformulations...

Optimal value function | Theoretical, Mathematical and Computational Physics | Demand adjustment problem | Bilevel programming | Mathematics | 90B06 | Optimality conditions | Mathematical Methods in Physics | 91A65 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Constraint qualifications | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | STABILITY | OPTIMIZATION | MATRIX ESTIMATION | Demand | Differential calculus | Mathematical analysis | Transportation | Programming | Optimization | Marketing | Mathematical programming

Optimal value function | Theoretical, Mathematical and Computational Physics | Demand adjustment problem | Bilevel programming | Mathematics | 90B06 | Optimality conditions | Mathematical Methods in Physics | 91A65 | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Constraint qualifications | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | STABILITY | OPTIMIZATION | MATRIX ESTIMATION | Demand | Differential calculus | Mathematical analysis | Transportation | Programming | Optimization | Marketing | Mathematical programming

Journal Article

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Exact quadratic convex reformulations of mixed-integer quadratically constrained problems

Mathematical Programming, ISSN 0025-5610, 7/2016, Volume 158, Issue 1, pp. 235 - 266

.... The resolution is based on the reformulation of the original problem (QP) into an equivalent quadratic problem whose continuous relaxation is convex, so that it...

Semidefinite programming | Theoretical, Mathematical and Computational Physics | Integer quadratic programming | Mathematics | 90C20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Equivalent convex reformulation | Combinatorics | Branch-and-bound algorithm | BRANCH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | GLOBAL OPTIMIZATION | ALGORITHM | SEMIDEFINITE | Algorithms | Studies | Integer programming | Mathematical programming | Branch & bound algorithms

Semidefinite programming | Theoretical, Mathematical and Computational Physics | Integer quadratic programming | Mathematics | 90C20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Equivalent convex reformulation | Combinatorics | Branch-and-bound algorithm | BRANCH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | GLOBAL OPTIMIZATION | ALGORITHM | SEMIDEFINITE | Algorithms | Studies | Integer programming | Mathematical programming | Branch & bound algorithms

Journal Article

Journal of mathematical imaging and vision, ISSN 1573-7683, 2019, Volume 61, Issue 8, pp. 1173 - 1196

...Journal of Mathematical Imaging and Vision (2019) 61:1173â€“1196 https://doi.org/10.1007/s10851-019-00893-0 Chanâ€“Vese Reformulation for Selective Image...

Mathematical Methods in Physics | Applications of Mathematics | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | MINIMIZATION | CONVEX | VARIATIONAL MODEL | OPTIMIZATION | ALGORITHMS | ACTIVE CONTOURS | VARIANT | MUMFORD-SHAH MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Image processing

Mathematical Methods in Physics | Applications of Mathematics | Signal,Image and Speech Processing | Computer Science | Image Processing and Computer Vision | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | MINIMIZATION | CONVEX | VARIATIONAL MODEL | OPTIMIZATION | ALGORITHMS | ACTIVE CONTOURS | VARIANT | MUMFORD-SHAH MODEL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Image processing

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 12/2009, Volume 44, Issue 3, pp. 363 - 372

...Comput Optim Appl (2009) 44: 363â€“372 DOI 10.1007/s10589-007-9158-1 On equivalent reformulations for absolute value equations Oleg Prokopyev Received: 10...

Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Statistics, general | Operations Research, Mathematical Programming | Linear complementarity problem | Absolute valueÂ equations | Optimization | Absolute value equations | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPLEXITY | Integer programming | Studies

Convex and Discrete Geometry | Operations Research/Decision Theory | Mathematics | Statistics, general | Operations Research, Mathematical Programming | Linear complementarity problem | Absolute valueÂ equations | Optimization | Absolute value equations | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPLEXITY | Integer programming | Studies

Journal Article

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A locationâ€“inventory supply chain problem: Reformulation and piecewise linearization

Computers & Industrial Engineering, ISSN 0360-8352, 12/2015, Volume 90, pp. 381 - 389

â€˘We study a two-echelon inventory management problem with multiple retailers.â€˘The problem is formulated as an MINLP.â€˘We propose an equivalent formulation with...

Supply chain | Integer programming | Locationâ€“inventory | Piecewise linearization | Location-inventory | SYSTEM | ALGORITHM | NETWORK DESIGN | MODEL | FORMULATION | LOT | LAGRANGIAN-RELAXATION APPROACH | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, INDUSTRIAL | Logistics | Mixed integer | Algorithms | Nonlinearity | Warehouses | Mathematical models | Optimization | Heuristic | Linearization

Supply chain | Integer programming | Locationâ€“inventory | Piecewise linearization | Location-inventory | SYSTEM | ALGORITHM | NETWORK DESIGN | MODEL | FORMULATION | LOT | LAGRANGIAN-RELAXATION APPROACH | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, INDUSTRIAL | Logistics | Mixed integer | Algorithms | Nonlinearity | Warehouses | Mathematical models | Optimization | Heuristic | Linearization

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 11/2013, Volume 57, Issue 3, pp. 843 - 861

...â€“Isoda function, and this is demonstrated to guarantee existence of a solution. Using this function, we present two constrained optimization reformulations of the generalized Nash equilibrium problem (GNEP for short...

91A10 | Optimization reformulations | 90C30 | Operations Research/Decision Theory | Regularized indicator NikaidĂ´â€“Isoda function | Normalized Nash equilibria | Computer Science, general | Quasi-variational inequality problem | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | Regularized indicator NikaidĂ´-Isoda function | Studies | Game theory | Mathematical models | Constraints | Minima | Mathematical analysis | Indicators

91A10 | Optimization reformulations | 90C30 | Operations Research/Decision Theory | Regularized indicator NikaidĂ´â€“Isoda function | Normalized Nash equilibria | Computer Science, general | Quasi-variational inequality problem | Generalized Nash equilibrium problem | Optimization | Economics / Management Science | Real Functions | Regularized indicator NikaidĂ´-Isoda function | Studies | Game theory | Mathematical models | Constraints | Minima | Mathematical analysis | Indicators

Journal Article

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Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

Operations research, ISSN 0030-364X, 8/2012, Volume 60, Issue 4, pp. 936 - 953

.... We study compact reformulations of the McRow model with polyhedral and conic descriptions of the weight regions...

Pareto optimality | weighted sum method | multicriterion optimization | multiexpert optimization | robust optimization | McRow | Conic sections | Optimal solutions | Objective functions | Mathematical vectors | Research design | Mathematical functions | Stochastic models | Pareto efficiency | Modeling | Crop economics | METHODS | CRITERIA | DESIGN | ENERGY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GROUP DECISION-SUPPORT | MANAGEMENT | ALGORITHM | CONVERGENCE | SYSTEMS | MULTIATTRIBUTE UTILITY MEASUREMENT | JUDGMENTS | Multiple criteria decision making | Usage | Mathematical optimization | Analysis

Pareto optimality | weighted sum method | multicriterion optimization | multiexpert optimization | robust optimization | McRow | Conic sections | Optimal solutions | Objective functions | Mathematical vectors | Research design | Mathematical functions | Stochastic models | Pareto efficiency | Modeling | Crop economics | METHODS | CRITERIA | DESIGN | ENERGY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GROUP DECISION-SUPPORT | MANAGEMENT | ALGORITHM | CONVERGENCE | SYSTEMS | MULTIATTRIBUTE UTILITY MEASUREMENT | JUDGMENTS | Multiple criteria decision making | Usage | Mathematical optimization | Analysis

Journal Article

Transportation science, ISSN 1526-5447, 2016, Volume 50, Issue 3, pp. 910 - 925

Train movements on railway lines are generally controlled by human dispatchers. Because disruptions often occur, dispatchers make real-time scheduling and...

integer programming | logic Bendersâ€™ decomposition | railway optimization | Integer programming | Logic Benders' decomposition | Railway optimization | TRANSPORTATION | COORDINATION | MODEL | ALGORITHMS | DECISIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RAILWAY STATIONS | logic Benders' decomposition | JUNCTIONS | DELAY MANAGEMENT | TRANSPORTATION SCIENCE & TECHNOLOGY | ROUTING TRAINS | WAIT | REAL-TIME | Railroads | Services | Reports | Management | Dispatchers (Transportation) | Analysis

integer programming | logic Bendersâ€™ decomposition | railway optimization | Integer programming | Logic Benders' decomposition | Railway optimization | TRANSPORTATION | COORDINATION | MODEL | ALGORITHMS | DECISIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RAILWAY STATIONS | logic Benders' decomposition | JUNCTIONS | DELAY MANAGEMENT | TRANSPORTATION SCIENCE & TECHNOLOGY | ROUTING TRAINS | WAIT | REAL-TIME | Railroads | Services | Reports | Management | Dispatchers (Transportation) | Analysis

Journal Article

Operations research, ISSN 1526-5463, 2018, Volume 66, Issue 3, pp. 849 - 869

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the...

copositive programming | two-stage decision problems | distributionally robust optimization | Two-stage decision problems | Copositive programming | Distributionally robust optimization | REGRESSION | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | APPROXIMATION | UNCERTAINTY | BINARY | Linear programming | Distribution (Probability theory) | Mathematical optimization | Analysis

copositive programming | two-stage decision problems | distributionally robust optimization | Two-stage decision problems | Copositive programming | Distributionally robust optimization | REGRESSION | OPTIMIZATION PROBLEMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MANAGEMENT | APPROXIMATION | UNCERTAINTY | BINARY | Linear programming | Distribution (Probability theory) | Mathematical optimization | Analysis

Journal Article