Journal of global optimization, ISSN 1573-2916, 2013, Volume 55, Issue 3, pp. 507 - 520

In this paper, we present a unified approach for studying convex composite multiobjective optimization problems via asymptotic analysis...

Weak Pareto optimal solution | Convex composite multiobjective optimization | 90C29 | 90C48 | Nonemptiness and compactness | Optimization | Economics / Management Science | 90C25 | Operations Research/Decision Theory | Computer Science, general | Asymptotic analysis | Proximal-type method | Real Functions | MATHEMATICS, APPLIED | ALGORITHMS | WEAKLY EFFICIENT SOLUTIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | NONEMPTINESS | SOLUTION SETS | OPTIMALITY CONDITIONS | COMPACTNESS | Studies | Mathematical models | Mathematics | Convex analysis | Pareto optimality | Asymptotic properties | Convergence

Weak Pareto optimal solution | Convex composite multiobjective optimization | 90C29 | 90C48 | Nonemptiness and compactness | Optimization | Economics / Management Science | 90C25 | Operations Research/Decision Theory | Computer Science, general | Asymptotic analysis | Proximal-type method | Real Functions | MATHEMATICS, APPLIED | ALGORITHMS | WEAKLY EFFICIENT SOLUTIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | NONEMPTINESS | SOLUTION SETS | OPTIMALITY CONDITIONS | COMPACTNESS | Studies | Mathematical models | Mathematics | Convex analysis | Pareto optimality | Asymptotic properties | Convergence

Journal Article

Journal of Zhejiang University SCIENCE A, ISSN 1673-565X, 10/2014, Volume 15, Issue 10, pp. 774 - 788

To improve the multiple performance indices of practical engineering structures under uncertainties, an interval constrained multiobjective optimization model was constructed with structural...

Interval multiobjective optimization | Uncertainty | Radial basis function (RBF) | Non-dominated sorting genetic algorithm (NSGA-II) | 不确定性 | Civil Engineering | 径向基函数 | 区间分析法 | TP391 | Classical Continuum Physics | Engineering | Interval analysis method | TH133.5 | 非支配排序遗传算法(NSGA-II) | 区间多目标优化 | Mechanical Engineering | Industrial Chemistry/Chemical Engineering | UNCERTAIN OPTIMIZATION | PHYSICS, APPLIED | ALGORITHM | DESIGN OPTIMIZATION | RELIABILITY | ENGINEERING, MULTIDISCIPLINARY | DECISION-MAKING | CONVEX MODELS | TOPOLOGY OPTIMIZATION | NUMBER PROGRAMMING METHOD | Performance indices | Finite element method | Intervals | Radial basis function | Construction | Mathematical analysis | Mathematical models | Optimization

Interval multiobjective optimization | Uncertainty | Radial basis function (RBF) | Non-dominated sorting genetic algorithm (NSGA-II) | 不确定性 | Civil Engineering | 径向基函数 | 区间分析法 | TP391 | Classical Continuum Physics | Engineering | Interval analysis method | TH133.5 | 非支配排序遗传算法(NSGA-II) | 区间多目标优化 | Mechanical Engineering | Industrial Chemistry/Chemical Engineering | UNCERTAIN OPTIMIZATION | PHYSICS, APPLIED | ALGORITHM | DESIGN OPTIMIZATION | RELIABILITY | ENGINEERING, MULTIDISCIPLINARY | DECISION-MAKING | CONVEX MODELS | TOPOLOGY OPTIMIZATION | NUMBER PROGRAMMING METHOD | Performance indices | Finite element method | Intervals | Radial basis function | Construction | Mathematical analysis | Mathematical models | Optimization

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/1997, Volume 95, Issue 1, pp. 209 - 224

.... In this paper, a convex composite multiobjective optimization problem, subject to a closed convex constraint set, is studied...

Multiobjective optimization | Calculus of Variations and Optimal Control | Mathematics | Theory of Computation | sufficient optimality condition | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | convex analysis | Optimization | nonsmooth analysis | Nonsmooth analysis | Sufficient optimality condition | Convex analysis

Multiobjective optimization | Calculus of Variations and Optimal Control | Mathematics | Theory of Computation | sufficient optimality condition | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | convex analysis | Optimization | nonsmooth analysis | Nonsmooth analysis | Sufficient optimality condition | Convex analysis

Journal Article

4.
Full Text
Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2010, Volume 144, Issue 1, pp. 29 - 42

For a given multiobjective optimization problem, we study recession properties of the sets of efficient solutions and properly efficient solutions...

Properly efficient solutions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Recession functions | Efficient solutions | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Recession cones | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIUM PROBLEMS | COMPACTNESS | CONVEX VECTOR OPTIMIZATION | PROPER EFFICIENCY | MAXIMIZATION | Studies | Mathematical problems | Vector space

Properly efficient solutions | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Recession functions | Efficient solutions | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Recession cones | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EQUILIBRIUM PROBLEMS | COMPACTNESS | CONVEX VECTOR OPTIMIZATION | PROPER EFFICIENCY | MAXIMIZATION | Studies | Mathematical problems | Vector space

Journal Article

Operations research, ISSN 1526-5463, 2014, Volume 62, Issue 3, pp. 680 - 695

.... In multiobjective linear optimization, given a solution that is not a weakly efficient solution to the forward problem, our method generates objective function weights that make the given solution...

Optimal solutions | Approximation | Objective functions | Urinary bladder | Oars | Rectum | Mathematical vectors | Radiotherapy | Treatment planning | METHODS | Femur head | Multiobjective linear optimization | Radiation therapy treatment planning | Inverse optimization | DISTRIBUTIONS | MODULATED RADIATION-THERAPY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | TREATMENT PLAN QUALITY | MANAGEMENT | CONVEX PARETO SURFACES | ALGORITHM | Usage | Care and treatment | Research | Mathematical optimization | Analysis | Cancer

Optimal solutions | Approximation | Objective functions | Urinary bladder | Oars | Rectum | Mathematical vectors | Radiotherapy | Treatment planning | METHODS | Femur head | Multiobjective linear optimization | Radiation therapy treatment planning | Inverse optimization | DISTRIBUTIONS | MODULATED RADIATION-THERAPY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | TREATMENT PLAN QUALITY | MANAGEMENT | CONVEX PARETO SURFACES | ALGORITHM | Usage | Care and treatment | Research | Mathematical optimization | Analysis | Cancer

Journal Article

Numerical heat transfer. Part B, Fundamentals, ISSN 1040-7790, 2012, Volume 61, Issue 6, pp. 439 - 470

...) with an aggregated objective function approach (AOF) to tackle this topology optimization problem through a multiobjective strategy...

SHAPE OPTIMIZATION | DESIGN | MECHANICS | BOUNDARY | THERMODYNAMICS | HEAT-CONDUCTION | Mathematical analysis | Pareto optimality | Topology optimization | Strategy | Mathematical models | Polymethyl methacrylates | Optimization | Variance | Engineering Sciences | domain_spi.energ

SHAPE OPTIMIZATION | DESIGN | MECHANICS | BOUNDARY | THERMODYNAMICS | HEAT-CONDUCTION | Mathematical analysis | Pareto optimality | Topology optimization | Strategy | Mathematical models | Polymethyl methacrylates | Optimization | Variance | Engineering Sciences | domain_spi.energ

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 11/2016, Volume 171, Issue 2, pp. 708 - 725

.... Then, the sufficient optimality conditions for a (weak) Pareto optimality of a feasible solution are established for the considered nonsmooth multiobjective optimization problem under assumptions that the involved functions are quasidifferentiable F...

Quasidifferentiable F -convexity with respect to a convex compact set | 90C29 | Mathematics | Theory of Computation | 90C26 | Optimization | Quasidifferentiable multiobjective optimization problem | Fritz John-type necessary optimality conditions | Karush–Kuhn–Tucker-type necessary optimality conditions | 90C30 | Calculus of Variations and Optimal Control; Optimization | 49J52 | Pareto optimality | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Quasidifferentiable F-convexity with respect to a convex compact set | Karush-Kuhn-Tucker-type necessary optimality conditions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SPACES | NONSMOOTH | Computer science | Pareto efficiency | Studies | Pareto optimum | Mathematical analysis | Differential equations | Multiple objective analysis | Paper | Feasibility | Inequalities

Quasidifferentiable F -convexity with respect to a convex compact set | 90C29 | Mathematics | Theory of Computation | 90C26 | Optimization | Quasidifferentiable multiobjective optimization problem | Fritz John-type necessary optimality conditions | Karush–Kuhn–Tucker-type necessary optimality conditions | 90C30 | Calculus of Variations and Optimal Control; Optimization | 49J52 | Pareto optimality | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Quasidifferentiable F-convexity with respect to a convex compact set | Karush-Kuhn-Tucker-type necessary optimality conditions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SPACES | NONSMOOTH | Computer science | Pareto efficiency | Studies | Pareto optimum | Mathematical analysis | Differential equations | Multiple objective analysis | Paper | Feasibility | Inequalities

Journal Article

Acta mathematica Hungarica, ISSN 1588-2632, 2007, Volume 116, Issue 3, pp. 177 - 196

Given a multiobjective optimization problem with the components of the objective function as well as the constraint functions being composed convex functions, we introduce, by using the Fenchel-Moreau...

optimality conditions | scalar duality | 90C46 | composed convex functions | 90C25 | Mathematics, general | 90C29 | Mathematics | multiobjective duality | Optimality conditions | Multiobjective duality | Composed convex functions | Scalar duality | MATHEMATICS | SUFFICIENT CONDITIONS | LOCAL MINIMUM | ORDER CONDITIONS

optimality conditions | scalar duality | 90C46 | composed convex functions | 90C25 | Mathematics, general | 90C29 | Mathematics | multiobjective duality | Optimality conditions | Multiobjective duality | Composed convex functions | Scalar duality | MATHEMATICS | SUFFICIENT CONDITIONS | LOCAL MINIMUM | ORDER CONDITIONS

Journal Article

Journal of optimization theory and applications, ISSN 1573-2878, 2013, Volume 159, Issue 1, pp. 125 - 137

In this paper, a subgradient-type method for solving nonsmooth multiobjective optimization problems on Riemannian manifolds is proposed and analyzed...

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Multiobjective optimization | Pareto optimality | Mathematics | Theory of Computation | Quasi-Féjer convergence | Applications of Mathematics | Engineering, general | Optimization | Subgradient method | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | STEEPEST DESCENT METHOD | ALGORITHM | SECTIONS | MONOTONE VECTOR-FIELDS | LOCAL CONVERGENCE | CONVEX-FUNCTIONS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Quasi-Fejer convergence | QUASI-CONVEX | Pareto efficiency | Analysis | Methods | Studies | Optimization techniques | Topological manifolds | Pareto optimum | Mathematical programming | Manifolds | Sequences | Mathematical analysis | Minimization | Curvature

Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Multiobjective optimization | Pareto optimality | Mathematics | Theory of Computation | Quasi-Féjer convergence | Applications of Mathematics | Engineering, general | Optimization | Subgradient method | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | STEEPEST DESCENT METHOD | ALGORITHM | SECTIONS | MONOTONE VECTOR-FIELDS | LOCAL CONVERGENCE | CONVEX-FUNCTIONS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Quasi-Fejer convergence | QUASI-CONVEX | Pareto efficiency | Analysis | Methods | Studies | Optimization techniques | Topological manifolds | Pareto optimum | Mathematical programming | Manifolds | Sequences | Mathematical analysis | Minimization | Curvature

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 8/2014, Volume 162, Issue 2, pp. 447 - 462

This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem (SIMOP, for short...

Semi-infinite optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Duality | Applications of Mathematics | Engineering, general | Necessary/sufficient condition | Generalized convex function | Positively properly efficient solution | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE OPTIMIZATION | CONSTRAINT QUALIFICATIONS | OPTIMALITY CONDITIONS | MINIMIZERS | Studies | Analysis | Mathematical analysis | Vectors (mathematics)

Semi-infinite optimization | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Mathematics | Theory of Computation | Duality | Applications of Mathematics | Engineering, general | Necessary/sufficient condition | Generalized convex function | Positively properly efficient solution | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE OPTIMIZATION | CONSTRAINT QUALIFICATIONS | OPTIMALITY CONDITIONS | MINIMIZERS | Studies | Analysis | Mathematical analysis | Vectors (mathematics)

Journal Article

Set-Valued Analysis, ISSN 0927-6947, 12/2006, Volume 14, Issue 4, pp. 327 - 345

We study sharp minima for multiobjective optimization problems. In terms of the Mordukhovich coderivative and the normal cone, we present sufficient...

multiobjective optimization | subdifferential | normal cone | sharp minimum | 49J52 | 90C29 | coderivative | Sharp minimum | Normal cone | Coderivative | Multiobjective optimization | Subdifferential | MATHEMATICS, APPLIED | CONSTANTS | STRONG UNIQUENESS | GAUSS-NEWTON METHOD | CONVEX COMPOSITE OPTIMIZATION | LINEAR INEQUALITIES | SYSTEMS | CONVERGENCE | ERROR-BOUNDS

multiobjective optimization | subdifferential | normal cone | sharp minimum | 49J52 | 90C29 | coderivative | Sharp minimum | Normal cone | Coderivative | Multiobjective optimization | Subdifferential | MATHEMATICS, APPLIED | CONSTANTS | STRONG UNIQUENESS | GAUSS-NEWTON METHOD | CONVEX COMPOSITE OPTIMIZATION | LINEAR INEQUALITIES | SYSTEMS | CONVERGENCE | ERROR-BOUNDS

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 9/2016, Volume 65, Issue 1, pp. 289 - 308

By using auxiliary principle technique, a new proximal point algorithm based on decomposition method is suggested for computing a weakly efficient solution of the constrained multiobjective optimization problem (MOP...

Auxiliary principle | Convex and Discrete Geometry | Decomposition method | Mathematics | Operations Research, Management Science | Multiobjective optimization with cone constraints | Operation Research/Decision Theory | Statistics, general | Proximal point algorithm | Optimization | Split feasibility problems | Mixed variational inequalities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SPLIT FEASIBILITY | ITERATIVE ALGORITHMS | CQ ALGORITHM | Medical colleges | Methods | Algorithms | Constraints | Computation | Feasibility | Mathematical models | Decomposition | Convergence

Auxiliary principle | Convex and Discrete Geometry | Decomposition method | Mathematics | Operations Research, Management Science | Multiobjective optimization with cone constraints | Operation Research/Decision Theory | Statistics, general | Proximal point algorithm | Optimization | Split feasibility problems | Mixed variational inequalities | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SPLIT FEASIBILITY | ITERATIVE ALGORITHMS | CQ ALGORITHM | Medical colleges | Methods | Algorithms | Constraints | Computation | Feasibility | Mathematical models | Decomposition | Convergence

Journal Article

CMES - Computer Modeling in Engineering and Sciences, ISSN 1526-1492, 2011, Volume 74, Issue 1, pp. 39 - 64

This paper studies the reliability-based multiobjective optimization by using a new interval strategy to model uncertain parameters...

Reliability-based optimization | Response surface method (RSM) | Approximation model | Multiobjective optimization | Satisfaction degree of interval | CONVEX MODEL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | CRASHWORTHINESS | NUMBER PROGRAMMING METHOD | NONPROBABILISTIC CONCEPT | RANKING | Multiple objective analysis | Approximation | Impact strength | Parameter uncertainty | Pareto optimization | Reliability engineering | Constraint modelling | Response surface methodology | Crashworthiness | Design optimization

Reliability-based optimization | Response surface method (RSM) | Approximation model | Multiobjective optimization | Satisfaction degree of interval | CONVEX MODEL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | CRASHWORTHINESS | NUMBER PROGRAMMING METHOD | NONPROBABILISTIC CONCEPT | RANKING | Multiple objective analysis | Approximation | Impact strength | Parameter uncertainty | Pareto optimization | Reliability engineering | Constraint modelling | Response surface methodology | Crashworthiness | Design optimization

Journal Article

Computational optimization and applications, ISSN 1573-2894, 2005, Volume 34, Issue 1, pp. 115 - 151

.... This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW...

multiobjective optimization | vehicle routing problems | Convex and Discrete Geometry | Operations Research/Decision Theory | evolutionary algorithms | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Optimization | Multiobjective optimization | Vehicle routing problems | Evolutionary algorithms | GENETIC ALGORITHMS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | METAHEURISTICS | SIZE | OPTIMIZATION | HEURISTICS | Algorithms | Studies | Linear programming | Mathematical models

multiobjective optimization | vehicle routing problems | Convex and Discrete Geometry | Operations Research/Decision Theory | evolutionary algorithms | Mathematics | Operations Research, Mathematical Programming | Statistics, general | Optimization | Multiobjective optimization | Vehicle routing problems | Evolutionary algorithms | GENETIC ALGORITHMS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | METAHEURISTICS | SIZE | OPTIMIZATION | HEURISTICS | Algorithms | Studies | Linear programming | Mathematical models

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2016, Volume 17, Issue 9, pp. 1791 - 1811

... and some iteration points to be infeasible to solve the optimization problems with explicit constraints...

Conic convex optimization problems | Local error bound | Strong Lagrangian multipliers | Generalized weak sharp minima | Generalized sharp minimum | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | MULTIOBJECTIVE OPTIMIZATION | STRONG UNIQUENESS | COMPOSITE OPTIMIZATION | GAUSS-NEWTON METHOD | VARIATIONAL-INEQUALITIES | MATHEMATICS | generalized sharp minimum | BANACH-SPACES | strong Lagrangian multipliers | ERROR-BOUNDS | local error bound | LINEAR REGULARITY | generalized weak sharp minima

Conic convex optimization problems | Local error bound | Strong Lagrangian multipliers | Generalized weak sharp minima | Generalized sharp minimum | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | MULTIOBJECTIVE OPTIMIZATION | STRONG UNIQUENESS | COMPOSITE OPTIMIZATION | GAUSS-NEWTON METHOD | VARIATIONAL-INEQUALITIES | MATHEMATICS | generalized sharp minimum | BANACH-SPACES | strong Lagrangian multipliers | ERROR-BOUNDS | local error bound | LINEAR REGULARITY | generalized weak sharp minima

Journal Article

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Generalized weak sharp minima in cone-constrained convex optimization with applications

Computational Optimization and Applications, ISSN 0926-6003, 12/2012, Volume 53, Issue 3, pp. 807 - 821

In this paper, we consider convex optimization problems with cone constraints (CPC in short). We study generalized weak sharp minima properties...

Cone-constrained convex programming | Operations Research/Decision Theory | Convex and Discrete Geometry | Robinson’s constraint qualification | Systems of differential inclusions | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | Generalized weak sharp minima | Tangent cone | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | SPACES | STRONG UNIQUENESS | COMPOSITE OPTIMIZATION | GAUSS-NEWTON METHOD | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | SOLUTION SETS | CONVERGENCE | ERROR-BOUNDS | Robinson's constraint qualification | Studies | Computer programming | Hilbert space | Algorithms | Convex analysis | Differential equations | Mathematical models | Minima | Criteria | Banach space | Convergence

Cone-constrained convex programming | Operations Research/Decision Theory | Convex and Discrete Geometry | Robinson’s constraint qualification | Systems of differential inclusions | Mathematics | Operations Research, Management Science | Statistics, general | Optimization | Generalized weak sharp minima | Tangent cone | MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | SPACES | STRONG UNIQUENESS | COMPOSITE OPTIMIZATION | GAUSS-NEWTON METHOD | VARIATIONAL-INEQUALITIES | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMS | SOLUTION SETS | CONVERGENCE | ERROR-BOUNDS | Robinson's constraint qualification | Studies | Computer programming | Hilbert space | Algorithms | Convex analysis | Differential equations | Mathematical models | Minima | Criteria | Banach space | Convergence

Journal Article

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, ISSN 0163-0563, 01/2014, Volume 35, Issue 1, pp. 1 - 19

.... These, moreover, really enable to derive for cone-constrained convex vector optimization problems, a complete epsilon-efficiency criterion of the Kuhn-Tucker type given...

MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | Cone-inequality constraints | CALCULUS | LAGRANGE MULTIPLIERS | CONVEX-FUNCTIONS | WEAK | MAPS | DUALITY | Approximate efficiency | Vector composites | Approximate vector subdifferentials | Vector optimization | OPTIMALITY

MATHEMATICS, APPLIED | MULTIOBJECTIVE OPTIMIZATION | Cone-inequality constraints | CALCULUS | LAGRANGE MULTIPLIERS | CONVEX-FUNCTIONS | WEAK | MAPS | DUALITY | Approximate efficiency | Vector composites | Approximate vector subdifferentials | Vector optimization | OPTIMALITY

Journal Article

Mathematical methods of operations research (Heidelberg, Germany), ISSN 1432-5217, 2006, Volume 64, Issue 3, pp. 521 - 540

We consider vector optimization problems on Banach spaces without convexity assumptions...

Lagrangian conditions | Mordukhovich subdifferential | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Non-convex vector optimization | Mathematics | Business/Management Science, general | Ioffe subdifferential | MATHEMATICS, APPLIED | APPROXIMATE SUBDIFFERENTIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE OPTIMIZATION | REGULARITY | CALCULUS | NONSMOOTH | non-convex vector optimization | Studies | Optimization techniques | Mathematical models | Banach spaces

Lagrangian conditions | Mordukhovich subdifferential | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Non-convex vector optimization | Mathematics | Business/Management Science, general | Ioffe subdifferential | MATHEMATICS, APPLIED | APPROXIMATE SUBDIFFERENTIALS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MULTIOBJECTIVE OPTIMIZATION | REGULARITY | CALCULUS | NONSMOOTH | non-convex vector optimization | Studies | Optimization techniques | Mathematical models | Banach spaces

Journal Article

Medical Physics, ISSN 0094-2405, 11/2018, Volume 45, Issue 11, pp. e1011 - e1023

Treatment planning for protons and heavier ions is adapting technologies originally developed for photon dose optimization, but also has to meet its particular challenges...

realiative biological effectiveness | treatment planning

realiative biological effectiveness | treatment planning