Computational Optimization and Applications, ISSN 0926-6003, 11/2018, Volume 71, Issue 2, pp. 403 - 433

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a...

Semidefinite programming | Robust optimization | Difference-of-convex programming | Concaveâ€“convex procedure | Operations Research/Decision Theory | Convex and Discrete Geometry | Complementarity constraint | Design-dependent load | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | EIGENVALUE | MATHEMATICS, APPLIED | Concave-convex procedure | DESIGN | STABILITY | ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SELECTION | STRESS | Topology optimization | Computational geometry | Convexity | Heuristic methods | Mathematical programming | Mathematics - Optimization and Control

Semidefinite programming | Robust optimization | Difference-of-convex programming | Concaveâ€“convex procedure | Operations Research/Decision Theory | Convex and Discrete Geometry | Complementarity constraint | Design-dependent load | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | EIGENVALUE | MATHEMATICS, APPLIED | Concave-convex procedure | DESIGN | STABILITY | ALGORITHMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SELECTION | STRESS | Topology optimization | Computational geometry | Convexity | Heuristic methods | Mathematical programming | Mathematics - Optimization and Control

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2011, Volume 21, Issue 3, pp. 833 - 863

We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy...

Applications in optimization | Mixed-integer nonlinear programming | Complementarity problems | MATHEMATICS, APPLIED | applications in optimization | mixed-integer nonlinear programming | GENETIC ALGORITHM | SCHEME | FRAMES | SQP | INELASTIC ANALYSIS | FLEXURAL DESIGN | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | CONVERGENCE | OPTIMIZATION | complementarity problems

Applications in optimization | Mixed-integer nonlinear programming | Complementarity problems | MATHEMATICS, APPLIED | applications in optimization | mixed-integer nonlinear programming | GENETIC ALGORITHM | SCHEME | FRAMES | SQP | INELASTIC ANALYSIS | FLEXURAL DESIGN | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | CONVERGENCE | OPTIMIZATION | complementarity problems

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 2/2010, Volume 46, Issue 2, pp. 217 - 232

In this paper, we present new convergence results of augmented Lagrangian methods for mathematical programs with complementarity constraints (MPCC). Modified...

Nonconvex constrained optimization | Modified augmented Lagrangian methods | Operations Research/Decision Theory | Mathematical program with complementarity constraints | Computer Science, general | Optimization | Convergence to global solution | Economics / Management Science | Real Functions | MATHEMATICS, APPLIED | ALGORITHM | SIMPLE BOUNDS | MULTIPLIERS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GLOBAL OPTIMIZATION | EQUILIBRIUM CONSTRAINTS | GENERAL CONSTRAINTS | OPTIMALITY | Management techniques | Management science | Management | Mathematical optimization | Methods | Studies | Algorithms | Mathematical programming

Nonconvex constrained optimization | Modified augmented Lagrangian methods | Operations Research/Decision Theory | Mathematical program with complementarity constraints | Computer Science, general | Optimization | Convergence to global solution | Economics / Management Science | Real Functions | MATHEMATICS, APPLIED | ALGORITHM | SIMPLE BOUNDS | MULTIPLIERS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GLOBAL OPTIMIZATION | EQUILIBRIUM CONSTRAINTS | GENERAL CONSTRAINTS | OPTIMALITY | Management techniques | Management science | Management | Mathematical optimization | Methods | Studies | Algorithms | Mathematical programming

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 02/2016, Volume 249, Issue 1, pp. 41 - 54

A Projected-Gradient Underdetermined Newton-like algorithm will be introduced for finding a solution of a Horizontal Nonlinear Complementarity Problem (HNCP)...

Nonlinear systems of equations | Global optimization | Nonlinear programming | Complementarity problems | Mathematical Programming with Complementarity Constraints | ELASTIC-MODE | REFORMULATION | NETWORKS | ELECTRICITY MARKETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR EQUATIONS | ACTIVE-SET ALGORITHM | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | OPTIMIZATION | GLOBAL CONVERGENCE | Combinatorial optimization | Analysis | Problem solving | Mathematical optimization

Nonlinear systems of equations | Global optimization | Nonlinear programming | Complementarity problems | Mathematical Programming with Complementarity Constraints | ELASTIC-MODE | REFORMULATION | NETWORKS | ELECTRICITY MARKETS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | NONLINEAR EQUATIONS | ACTIVE-SET ALGORITHM | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | OPTIMIZATION | GLOBAL CONVERGENCE | Combinatorial optimization | Analysis | Problem solving | Mathematical optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 5/2019, Volume 181, Issue 2, pp. 504 - 520

One of the most commonly used methods for solving bilevel programming problems (whose lower level problem is convex) starts with reformulating it as a...

Mathematical programming with complementarity constraints | Pessimistic approach | Bilevel problem | Mathematics | Theory of Computation | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | 90C47 | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical analysis | Minimax technique | Mathematical programming

Mathematical programming with complementarity constraints | Pessimistic approach | Bilevel problem | Mathematics | Theory of Computation | Optimization | 90C30 | Calculus of Variations and Optimal Control; Optimization | 90C47 | Operations Research/Decision Theory | 90C33 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Mathematical analysis | Minimax technique | Mathematical programming

Journal Article

Baltic Journal of Modern Computing, ISSN 2255-8942, 01/2014, Volume 2, Issue 4, pp. 248 - 248

In this paper, we consider an optimization problem arising in multidimensional scaling with city-block distances. The objective function of this problem has...

Algorithms | Computation | Mathematical analysis | Mathematical models | Quadratic programming | Optimization

Algorithms | Computation | Mathematical analysis | Mathematical models | Quadratic programming | Optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2006, Volume 131, Issue 1, pp. 89 - 113

A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasistatic frictional contact...

arc-length method | mathematical program with complementarity constraints | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Contact problems | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | maximum dissipation | Coulombâ€™s friction | Optimization | Coulomb's friction | Mathematical program with complementarity constraints | Arc-length method | Maximum dissipation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | contact problems | Studies | Mathematical programming | Energy of formation | Mathematical analysis | Dissipation | Mathematical models | Nonlinear programming | Regularization | Contact

arc-length method | mathematical program with complementarity constraints | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Contact problems | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | maximum dissipation | Coulombâ€™s friction | Optimization | Coulomb's friction | Mathematical program with complementarity constraints | Arc-length method | Maximum dissipation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | contact problems | Studies | Mathematical programming | Energy of formation | Mathematical analysis | Dissipation | Mathematical models | Nonlinear programming | Regularization | Contact

Journal Article

Computers and Chemical Engineering, ISSN 0098-1354, 01/2015, Volume 72, pp. 3 - 20

Despite the economic benefits of flowsheet optimization, many commercial tools suffer from long computational times, limited problem formulation flexibility...

Distillation | Air separation unit | Mathematical programming with complementarity constraints | Process optimization | Coal oxycombustion | Heat integration | AZEOTROPIC MIXTURES | NUMBER | OPTIMAL-DESIGN | Mathematical programming with | ENGINEERING, CHEMICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | complementarity constraints | DISTILLATION-COLUMNS | TRAYS | AIR SEPARATION | UNITS | DISJUNCTIVE PROGRAMMING-MODELS | Thermodynamics | Algorithms | Electric power-plants | Analysis | Power plants | Economics | Thermodynamic models | Mathematical analysis | Coal | Mathematical models | Optimization

Distillation | Air separation unit | Mathematical programming with complementarity constraints | Process optimization | Coal oxycombustion | Heat integration | AZEOTROPIC MIXTURES | NUMBER | OPTIMAL-DESIGN | Mathematical programming with | ENGINEERING, CHEMICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTEGRATION | complementarity constraints | DISTILLATION-COLUMNS | TRAYS | AIR SEPARATION | UNITS | DISJUNCTIVE PROGRAMMING-MODELS | Thermodynamics | Algorithms | Electric power-plants | Analysis | Power plants | Economics | Thermodynamic models | Mathematical analysis | Coal | Mathematical models | Optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2004, Volume 123, Issue 2, p. 365

Â We adapt the convergence analysis of the smoothing (Ref. 1) and regularization (Ref. 2) methods to a penalty framework for mathematical programs with...

Studies | Optimization | Mathematical programming

Studies | Optimization | Mathematical programming

Journal Article

Mathematical Programming, ISSN 0025-5610, 12/2013, Volume 142, Issue 1, pp. 539 - 577

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear minâ€“max problems which...

Mathematical programming with complementarity constraints | Semi-infinite optimization | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | Bilevel optimization | Robust optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C47 | Numerical Analysis | 90C55 | 90C34 | Sequential convex programming | Combinatorics | MIN-MAX PROBLEMS | MATHEMATICS, APPLIED | LINEAR COMPLEMENTARITY CONSTRAINTS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SQP | CONVERGENT ALGORITHM | MATHEMATICAL PROGRAMS | GLOBAL OPTIMIZATION | EQUILIBRIUM CONSTRAINTS | GENERALIZED SEMIINFINITE OPTIMIZATION | OPTIMALITY | Relaxation | Algorithms | Studies | Analysis | Optimization | Mathematical programming

Mathematical programming with complementarity constraints | Semi-infinite optimization | Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | Bilevel optimization | Robust optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C47 | Numerical Analysis | 90C55 | 90C34 | Sequential convex programming | Combinatorics | MIN-MAX PROBLEMS | MATHEMATICS, APPLIED | LINEAR COMPLEMENTARITY CONSTRAINTS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SQP | CONVERGENT ALGORITHM | MATHEMATICAL PROGRAMS | GLOBAL OPTIMIZATION | EQUILIBRIUM CONSTRAINTS | GENERALIZED SEMIINFINITE OPTIMIZATION | OPTIMALITY | Relaxation | Algorithms | Studies | Analysis | Optimization | Mathematical programming

Journal Article

Mathematical Programming, ISSN 0025-5610, 12/2012, Volume 136, Issue 1, pp. 183 - 207

A numerical solution method for semi-infinite optimization problems with arbitrary, not necessarily box-shaped, index sets is presented. Following the ideas of...

Mathematical programming with complementarity constraints | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Semi-infinite programming | Mathematical Methods in Physics | Global optimization | Bilevel optimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Numerical Analysis | 90C33 | 90C34 | Combinatorics | Î±BB | SEARCH FILTER METHODS | C-2-CONTINUOUS PROBLEMS | MATHEMATICS, APPLIED | DESIGN | DIFFERENTIABLE CONSTRAINED NLPS | TIGHT CONVEX UNDERESTIMATORS | GLOBAL OPTIMIZATION METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALPHA-BB | SCHEME | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | alpha BB | MATHEMATICAL PROGRAMS | CONVERGENCE | Studies | Optimization | Mathematical programming | Construction | Algorithms | Approximation | Mathematical analysis | Adaptive algorithms | Programming | Mathematical models

Mathematical programming with complementarity constraints | 65K05 | Theoretical, Mathematical and Computational Physics | Mathematics | 90C26 | Semi-infinite programming | Mathematical Methods in Physics | Global optimization | Bilevel optimization | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Convex optimization | Numerical Analysis | 90C33 | 90C34 | Combinatorics | Î±BB | SEARCH FILTER METHODS | C-2-CONTINUOUS PROBLEMS | MATHEMATICS, APPLIED | DESIGN | DIFFERENTIABLE CONSTRAINED NLPS | TIGHT CONVEX UNDERESTIMATORS | GLOBAL OPTIMIZATION METHOD | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALPHA-BB | SCHEME | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | alpha BB | MATHEMATICAL PROGRAMS | CONVERGENCE | Studies | Optimization | Mathematical programming | Construction | Algorithms | Approximation | Mathematical analysis | Adaptive algorithms | Programming | Mathematical models

Journal Article

12.
Full Text
Complementarity model for load tap changing transformers in stability based OPF problem

Electric Power Systems Research, ISSN 0378-7796, 2006, Volume 76, Issue 6, pp. 592 - 599

The paper presents a stability optimal power flow (OPF) based problem that incorporates complementarity models for load tap changing transformers (LTCs). The...

Voltage stability | Mathematical programming with complementarity constraints | Optimal power flow | Load tap changing transformers | optimal power flow | load tap changing transformers | SYSTEMS | voltage stability | mathematical programming with complementarity constraints | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric transformers | Analysis

Voltage stability | Mathematical programming with complementarity constraints | Optimal power flow | Load tap changing transformers | optimal power flow | load tap changing transformers | SYSTEMS | voltage stability | mathematical programming with complementarity constraints | ENGINEERING, ELECTRICAL & ELECTRONIC | Electric transformers | Analysis

Journal Article

Optimization Methods and Software, ISSN 1055-6788, 02/2012, Volume 27, Issue 1, pp. 89 - 114

We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear...

pivoting method | linear program with complementarity constraints | 65K15 | 90C49 | complementarity constraints | 90C33 | MATHEMATICS, APPLIED | ELASTIC-MODE | SQP METHODS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | LU DECOMPOSITION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PERFORMANCE PROFILES | MODIFIED SIMPLEX APPROACH | ACTIVE-SET ALGORITHM | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | CUT ALGORITHM | OPTIMALITY CONDITIONS | Studies | Linear programming | Algorithms | Mathematical analysis | Searching | Simplex method | Software | Optimization | Computer programs

pivoting method | linear program with complementarity constraints | 65K15 | 90C49 | complementarity constraints | 90C33 | MATHEMATICS, APPLIED | ELASTIC-MODE | SQP METHODS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | LU DECOMPOSITION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PERFORMANCE PROFILES | MODIFIED SIMPLEX APPROACH | ACTIVE-SET ALGORITHM | MATHEMATICAL PROGRAMS | EQUILIBRIUM CONSTRAINTS | CUT ALGORITHM | OPTIMALITY CONDITIONS | Studies | Linear programming | Algorithms | Mathematical analysis | Searching | Simplex method | Software | Optimization | Computer programs

Journal Article

Journal of Industrial and Management Optimization, ISSN 1547-5816, 2018, Volume 14, Issue 2, pp. 625 - 636

Quadratic programs with complementarity constraints (QPCC) are NP-hard due to the nonconvexity of complementarity relation between the pairs of nonnegative...

Augmented Lagrangian method | Semidefinite programming | Doubly nonnegative relaxation | Branch and bound | Quadratic programs with complementarity constraints | augmented Lagrangian method | REFORMULATION | BINARY | branch and bound | RELAXATION | doubly nonnegative relaxation | semidefinite programming | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MATHEMATICAL PROGRAMS | COMPLEXITY | INEQUALITY CONSTRAINTS

Augmented Lagrangian method | Semidefinite programming | Doubly nonnegative relaxation | Branch and bound | Quadratic programs with complementarity constraints | augmented Lagrangian method | REFORMULATION | BINARY | branch and bound | RELAXATION | doubly nonnegative relaxation | semidefinite programming | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MATHEMATICAL PROGRAMS | COMPLEXITY | INEQUALITY CONSTRAINTS

Journal Article

Proceedings of the International Conference on learning and optimization algorithms: theory and applications, 05/2018, pp. 1 - 6

This paper aims at developing a new effective approach for solving mathematical programs with complementarity constraints (MPCCs). These mathematical programs...

Mathematical programming with complementarity constraints | Stationarity | Regularization | Penalty method

Mathematical programming with complementarity constraints | Stationarity | Regularization | Penalty method

Conference Proceeding

TOP, ISSN 1134-5764, 4/2012, Volume 20, Issue 1, pp. 4 - 25

Linear programming with linear complementarity constraints (LPLCC) is an area of active research in Optimization, due to its many applications, algorithms, and...

Industrial and Production Engineering | 90C26 | Complementarity problems | Optimization | Economics / Management Science | Global optimization | Mathematical programming with linear complementarity constraints | 90C30 | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 90C33 | Game Theory/Mathematical Methods | Nonlinear programming | BRANCH | STATIONARY POINT | ELASTIC-MODE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICAL PROGRAMS | BOUND ALGORITHM | CUT ALGORITHM | CONVERGENCE | OPTIMALITY CONDITIONS

Industrial and Production Engineering | 90C26 | Complementarity problems | Optimization | Economics / Management Science | Global optimization | Mathematical programming with linear complementarity constraints | 90C30 | Statistics for Business/Economics/Mathematical Finance/Insurance | Operations Research/Decision Theory | 90C33 | Game Theory/Mathematical Methods | Nonlinear programming | BRANCH | STATIONARY POINT | ELASTIC-MODE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICAL PROGRAMS | BOUND ALGORITHM | CUT ALGORITHM | CONVERGENCE | OPTIMALITY CONDITIONS

Journal Article

Computer Aided Chemical Engineering, ISSN 1570-7946, 2014, Volume 34, pp. 501 - 506

In this paper we apply an equation-oriented (EO) optimization framework to design ASU and CPU systems for coal oxycombustion power plants. Emphasis is placed...

Cryogenic air separation units | Flowsheet optimization | Heat integration | Nonlinear mathematical programming with complementarity constraints

Cryogenic air separation units | Flowsheet optimization | Heat integration | Nonlinear mathematical programming with complementarity constraints

Journal Article

18.
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Comments on: Algorithms for linear programming with linear complementarity constraints

TOP, ISSN 1134-5764, 4/2012, Volume 20, Issue 1, pp. 26 - 27

Journal Article

19.
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Comments on: Algorithms for linear programming with linear complementarity constraints

TOP, ISSN 1134-5764, 4/2012, Volume 20, Issue 1, pp. 28 - 29

Journal Article