ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, ISSN 0168-9673, 10/2014, Volume 30, Issue 4, pp. 845 - 858

In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of...

efficient solution | MATHEMATICS, APPLIED | scalarization | VARIATIONAL INEQUALITY | perturbed vector equilibrium problem | Painleve-Kuratowski convergence | GENERALIZED SYSTEMS | CONTINUITY | CONNECTEDNESS | LOWER SEMICONTINUITY | OPTIMIZATION | stability | EFFICIENT SOLUTIONS

efficient solution | MATHEMATICS, APPLIED | scalarization | VARIATIONAL INEQUALITY | perturbed vector equilibrium problem | Painleve-Kuratowski convergence | GENERALIZED SYSTEMS | CONTINUITY | CONNECTEDNESS | LOWER SEMICONTINUITY | OPTIMIZATION | stability | EFFICIENT SOLUTIONS

Journal Article

应用数学学报：英文版, ISSN 0168-9673, 2014, Volume 30, Issue 4, pp. 845 - 858

In this paper, we obtain some stability results for perturbed vector equilibrium problems. Under new assumptions, which are weaker than the assumption of...

向量均衡问题 | 线性度量空间 | 非单调性 | 严格单调性 | 弱有效解集 | efficient solution | Painlevé-Kuratowski convergence | 49K40 | 34D10 | Theoretical, Mathematical and Computational Physics | 90C33 | scalarization | Mathematics | Applications of Mathematics | Math Applications in Computer Science | stability | perturbed vector equilibrium problem

向量均衡问题 | 线性度量空间 | 非单调性 | 严格单调性 | 弱有效解集 | efficient solution | Painlevé-Kuratowski convergence | 49K40 | 34D10 | Theoretical, Mathematical and Computational Physics | 90C33 | scalarization | Mathematics | Applications of Mathematics | Math Applications in Computer Science | stability | perturbed vector equilibrium problem

Journal Article

Mathematical Sciences, ISSN 2008-1359, 6/2016, Volume 10, Issue 1, pp. 41 - 45

The lower semicontinuity of the (weak) efficient solution mappings for parametric vector equilibrium problems under more weaker assumptions is established....

90C31 | Lower semicontinuity | 49K40 | Cone lower semicontinuity | Order-perturbed parametric vector equilibrium problems | Efficient solutions | Mathematics | Applications of Mathematics | Mathematical analysis | Mapping | Vectors (mathematics)

90C31 | Lower semicontinuity | 49K40 | Cone lower semicontinuity | Order-perturbed parametric vector equilibrium problems | Efficient solutions | Mathematics | Applications of Mathematics | Mathematical analysis | Mapping | Vectors (mathematics)

Journal Article

New Trends in Mathematical Science, ISSN 2147-5520, 03/2020, Volume 1, Issue 7, pp. 79 - 89

In this work, we considered perurbed vector equilibrium problems involving set-valued monotone mapping and prove some existence results with and without...

Perturbed vector equilibrium problems | monotone mapping and KKM map | C- lower semicontinuity | self-segment-dense set

Perturbed vector equilibrium problems | monotone mapping and KKM map | C- lower semicontinuity | self-segment-dense set

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2016, Volume 17, Issue 8, pp. 1607 - 1625

Here, we consider two extensions of the notions M-well-posedness and B-well-posedness under perturbations for quasi-equilibrium problems. We establish some...

Vector quasi-equilibrium | Vector quasi-variational inequalities | M-well-posedness | B-well-posedness | Perturbed optimization | MATHEMATICS, APPLIED | CONVEXITY | SPACES | vector quasi-variational inequalities | MATHEMATICS | perturbed optimization | CONSTRAINTS | INCLUSION | VARIATIONAL-LIKE INEQUALITIES | SET OPTIMIZATION PROBLEMS

Vector quasi-equilibrium | Vector quasi-variational inequalities | M-well-posedness | B-well-posedness | Perturbed optimization | MATHEMATICS, APPLIED | CONVEXITY | SPACES | vector quasi-variational inequalities | MATHEMATICS | perturbed optimization | CONSTRAINTS | INCLUSION | VARIATIONAL-LIKE INEQUALITIES | SET OPTIMIZATION PROBLEMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 343, Issue 1, pp. 531 - 545

The goal of this paper is to prove some general vector-valued perturbed equilibrium principles and some existence results of vector equilibrium points for...

Vector-valued perturbed equilibrium principles | Lower semi-continuity | Variational principles | Equilibrium problems | equilibrium problems | MATHEMATICS | MATHEMATICS, APPLIED | vector-valued perturbed equilibrium principles | VARIATIONAL PRINCIPLE | variational principles | lower semi-continuity

Vector-valued perturbed equilibrium principles | Lower semi-continuity | Variational principles | Equilibrium problems | equilibrium problems | MATHEMATICS | MATHEMATICS, APPLIED | vector-valued perturbed equilibrium principles | VARIATIONAL PRINCIPLE | variational principles | lower semi-continuity

Journal Article

Open Mathematics, ISSN 2391-5455, 03/2018, Volume 16, Issue 1, pp. 276 - 288

In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological...

Vector equilibrium problem | 47J20 | 26B25 | Perturbed equilibrium problem | 90C33 | Primal-dual equilibrium problem | MATHEMATICS | EKELANDS PRINCIPLE | SETS | PSEUDOMONOTONE VARIATIONAL-INEQUALITIES | EXISTENCE THEOREMS

Vector equilibrium problem | 47J20 | 26B25 | Perturbed equilibrium problem | 90C33 | Primal-dual equilibrium problem | MATHEMATICS | EKELANDS PRINCIPLE | SETS | PSEUDOMONOTONE VARIATIONAL-INEQUALITIES | EXISTENCE THEOREMS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 04/2014, Volume 232, pp. 908 - 918

In this paper, we first establish sufficient conditions for the local uniqueness and Hölder continuity of perturbed solution set for a scalar optimization...

Pompeiu–Hausdorff metric | Parametric optimization problems | Hölder continuity | Perturbed solution sets | Pompeiu-Hausdorff metric | Holder continuity | MATHEMATICS, APPLIED | STABILITY | SENSITIVITY | VECTOR EQUILIBRIUM PROBLEMS | VARIATIONAL INEQUALITY | LOWER SEMICONTINUITY

Pompeiu–Hausdorff metric | Parametric optimization problems | Hölder continuity | Perturbed solution sets | Pompeiu-Hausdorff metric | Holder continuity | MATHEMATICS, APPLIED | STABILITY | SENSITIVITY | VECTOR EQUILIBRIUM PROBLEMS | VARIATIONAL INEQUALITY | LOWER SEMICONTINUITY

Journal Article

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, ISSN 1345-4773, 2014, Volume 15, Issue 6, pp. 1249 - 1259

In this paper, under new assumptions, which are weaker than the assumption of C-strictly monotone mapping, we obtain the Painleve-Kuratowski convergence of the...

MATHEMATICS, APPLIED | TRIFUNCTIONS | perturbed generalized systems | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | VARIATIONAL INEQUALITY | MATHEMATICS | Painleve-Kuratowski convergence | global efficient solution sets | CONTINUITY | FAN INEQUALITY PROBLEMS | CONNECTEDNESS | weak efficient solution sets | OPTIMIZATION | EFFICIENT SOLUTIONS | SEMICONTINUITY | Weak efficient solution sets | Painlevé-Kuratowski convergence | Perturbed generalized systems | Global efficient solution sets

MATHEMATICS, APPLIED | TRIFUNCTIONS | perturbed generalized systems | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | VARIATIONAL INEQUALITY | MATHEMATICS | Painleve-Kuratowski convergence | global efficient solution sets | CONTINUITY | FAN INEQUALITY PROBLEMS | CONNECTEDNESS | weak efficient solution sets | OPTIMIZATION | EFFICIENT SOLUTIONS | SEMICONTINUITY | Weak efficient solution sets | Painlevé-Kuratowski convergence | Perturbed generalized systems | Global efficient solution sets

Journal Article

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Painleve-Kuratowski Convergences of the Solution Sets to Perturbed Generalized Systems

应用数学学报：英文版, ISSN 0168-9673, 2012, Volume 28, Issue 2, pp. 361 - 370

In this paper, we obtain the Painleve-Kuratowski Convergence of the efficient solution sets, the weak efficient solution sets and various proper efficient...

收敛集 | 广义系统 | 弱有效解集 | 局部凸 | Hausdorff拓扑向量空间 | 映射序列 | Painlevé-Kuratowski convergence | 54A20 | 34D10 | Theoretical, Mathematical and Computational Physics | perturbed generalized systems | 90C33 | Scalarization | Mathematics | continuous convergence | Applications of Mathematics | Math Applications in Computer Science | Gamma-convergence | MATHEMATICS, APPLIED | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | Painleve-Kuratowski convergence | CONTINUITY | CONNECTEDNESS | OPTIMIZATION | EFFICIENT SOLUTIONS | SEMICONTINUITY

收敛集 | 广义系统 | 弱有效解集 | 局部凸 | Hausdorff拓扑向量空间 | 映射序列 | Painlevé-Kuratowski convergence | 54A20 | 34D10 | Theoretical, Mathematical and Computational Physics | perturbed generalized systems | 90C33 | Scalarization | Mathematics | continuous convergence | Applications of Mathematics | Math Applications in Computer Science | Gamma-convergence | MATHEMATICS, APPLIED | STABILITY | VECTOR EQUILIBRIUM PROBLEMS | Painleve-Kuratowski convergence | CONTINUITY | CONNECTEDNESS | OPTIMIZATION | EFFICIENT SOLUTIONS | SEMICONTINUITY

Journal Article

11.
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Painlev,-Kuratowski Stability of the Solution Sets to Perturbed Vector Generalized Systems

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, ISSN 0168-9673, 03/2018, Volume 34, Issue 2, pp. 304 - 317

In this paper, stability results of solution mappings to perturbed vector generalized system are studied. Firstly, without the assumption of monotonicity, the...

EXISTENCE | MATHEMATICS, APPLIED | perturbed generalized systems | PAINLEVE-KURATOWSKI CONVERGENCES | Painleve-Kuratowski convergence | global efficient solution sets | efficient solution sets | CONTINUITY | FAN INEQUALITY PROBLEMS | CONNECTEDNESS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | VALUED FUNCTIONS | EFFICIENT SOLUTIONS | SEMICONTINUITY

EXISTENCE | MATHEMATICS, APPLIED | perturbed generalized systems | PAINLEVE-KURATOWSKI CONVERGENCES | Painleve-Kuratowski convergence | global efficient solution sets | efficient solution sets | CONTINUITY | FAN INEQUALITY PROBLEMS | CONNECTEDNESS | OPTIMIZATION | EQUILIBRIUM PROBLEMS | VALUED FUNCTIONS | EFFICIENT SOLUTIONS | SEMICONTINUITY

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2014, Volume 37, Issue 1, pp. 106 - 122

We consider a periodically perforated domain obtained by making in R n a periodic set of holes, each of them of size proportional to ε . Then, we introduce a...

linearized elastostatics | periodically perforated domain | nonlinear boundary value problems for linear elliptic equations | singularly perturbed domain | integral representations, integral operators, integral equation methods | real analytic continuation in Banach space | MATHEMATICS, APPLIED | EFFECTIVE CONDUCTIVITY | integral representations | integral equation methods | integral operators | COMPOSITE | Boundaries | Mathematics - Analysis of PDEs

linearized elastostatics | periodically perforated domain | nonlinear boundary value problems for linear elliptic equations | singularly perturbed domain | integral representations, integral operators, integral equation methods | real analytic continuation in Banach space | MATHEMATICS, APPLIED | EFFECTIVE CONDUCTIVITY | integral representations | integral equation methods | integral operators | COMPOSITE | Boundaries | Mathematics - Analysis of PDEs

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 17

In this article, we introduce a perturbed system of generalized mixed quasi-equilibrium-like problems involving multi-valued mappings in Hilbert spaces. To...

perturbed system | 65K15 | convergence | Mathematics | 35M87 | 90C33 | 49J40 | Analysis | Mathematics, general | Applications of Mathematics | quasi-equilibrium-like | 47H05 | algorithm | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | THEOREMS | VARIATIONAL-LIKE INEQUALITIES | Mathematical analysis | Uniqueness | Inequalities | Hilbert space | Iterative algorithms | Mapping | Convergence | Research

perturbed system | 65K15 | convergence | Mathematics | 35M87 | 90C33 | 49J40 | Analysis | Mathematics, general | Applications of Mathematics | quasi-equilibrium-like | 47H05 | algorithm | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | THEOREMS | VARIATIONAL-LIKE INEQUALITIES | Mathematical analysis | Uniqueness | Inequalities | Hilbert space | Iterative algorithms | Mapping | Convergence | Research

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 05/2011, Volume 17, Issue 5, pp. 841 - 857

We consider quasilinear dynamic systems of the form where is a time scale, and provide extensions of a theorem of Wintner on systems with asymptotic...

Schauder fixed point theorem | time scale | asymptotic equilibrium | dynamic systems | Time scale | Dynamic systems | Asymptotic equilibrium | PERTURBED LINEAR-SYSTEMS | MATHEMATICS, APPLIED | BEHAVIOR | STABILITY | DIFFERENTIAL-EQUATIONS | CONSTANT SOLUTIONS | EQUIVALENCE | Asymptotic methods | Theorems | Differential equations | Difference equations | Asymptotic properties | Dynamics | Mathematical analysis | Vectors (mathematics) | Dynamical systems

Schauder fixed point theorem | time scale | asymptotic equilibrium | dynamic systems | Time scale | Dynamic systems | Asymptotic equilibrium | PERTURBED LINEAR-SYSTEMS | MATHEMATICS, APPLIED | BEHAVIOR | STABILITY | DIFFERENTIAL-EQUATIONS | CONSTANT SOLUTIONS | EQUIVALENCE | Asymptotic methods | Theorems | Differential equations | Difference equations | Asymptotic properties | Dynamics | Mathematical analysis | Vectors (mathematics) | Dynamical systems

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 01/2012, Volume 89, Issue 2, pp. 135 - 153

In this paper, explicit formulas for second order derivatives of the residual vector with respect to the state variables for a geometrically exact 3D beam...

Newton'smethod | equilibrium equations | critical points | geometrically exact kinematics | Reissner's beam model | rotation manifold | Equilibrium equations | Rotation manifold | Geometrically exact kinematics | Critical points | PATH | PERTURBED BIFURCATION THEORY | ALGORITHM | IMPLEMENTATION | MODEL | FORMULATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ROTATIONS | DYNAMICS | FINITE-ELEMENT | STABILITY POINTS

Newton'smethod | equilibrium equations | critical points | geometrically exact kinematics | Reissner's beam model | rotation manifold | Equilibrium equations | Rotation manifold | Geometrically exact kinematics | Critical points | PATH | PERTURBED BIFURCATION THEORY | ALGORITHM | IMPLEMENTATION | MODEL | FORMULATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | ROTATIONS | DYNAMICS | FINITE-ELEMENT | STABILITY POINTS

Journal Article

Cybernetics and Systems Analysis, ISSN 1060-0396, 9/2014, Volume 50, Issue 5, pp. 712 - 717

The influence of perturbations of initial data on the solutions of multicriteria optimization problems is considered. The properties of perturbed cones, which...

Processor Architectures | perturbation of initial data | perturbed ordering cones | Systems Theory, Control | Artificial Intelligence (incl. Robotics) | Software Engineering/Programming and Operating Systems | Mathematics | vector optimization problems

Processor Architectures | perturbation of initial data | perturbed ordering cones | Systems Theory, Control | Artificial Intelligence (incl. Robotics) | Software Engineering/Programming and Operating Systems | Mathematics | vector optimization problems

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2007, Volume 12, Issue 2, pp. 117 - 194

This paper systematically presents a theory for -dimensional nonlinear dynamics on continuous vector fields. In this paper, a different view to look into the...

First integral quantity increment | First integral manifold surface | Global transversality and tangency | Strange attractor fragmentation | Strong and weak stabilities | Limit cycles | Perturbed Hamiltonian systems | Nonlinear dynamic systems | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Mechanical engineering | Analysis

First integral quantity increment | First integral manifold surface | Global transversality and tangency | Strange attractor fragmentation | Strong and weak stabilities | Limit cycles | Perturbed Hamiltonian systems | Nonlinear dynamic systems | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Mechanical engineering | Analysis

Journal Article

Astrophysics and Space Science, ISSN 0004-640X, 11/2012, Volume 342, Issue 1, pp. 45 - 53

In this paper, we prove that the locations of the triangular points and their linear stability are affected by the oblateness of the more massive primary in...

Oblate spheroid | Extraterrestrial Physics, Space Sciences | Astrophysics and Astroparticles | Astrobiology | Restricted three-body problem | Cosmology | Stability of triangular points | Critical mass | Physics | Astronomy, Observations and Techniques | CHARACTERISTIC EXPONENTS | NONLINEAR STABILITY | ASTRONOMY & ASTROPHYSICS | LIBRATION POINTS | EQUILIBRIUM | PERTURBED POTENTIALS | Orbits | Numerical analysis | Astrophysics | Solar systems | Mathematical models | Planets | Stability | Solar system

Oblate spheroid | Extraterrestrial Physics, Space Sciences | Astrophysics and Astroparticles | Astrobiology | Restricted three-body problem | Cosmology | Stability of triangular points | Critical mass | Physics | Astronomy, Observations and Techniques | CHARACTERISTIC EXPONENTS | NONLINEAR STABILITY | ASTRONOMY & ASTROPHYSICS | LIBRATION POINTS | EQUILIBRIUM | PERTURBED POTENTIALS | Orbits | Numerical analysis | Astrophysics | Solar systems | Mathematical models | Planets | Stability | Solar system

Journal Article

19.
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Multi‐criteria optimization for parameterization of SAFT‐type equations of state for water

AIChE Journal, ISSN 0001-1541, 01/2018, Volume 64, Issue 1, pp. 226 - 237

Finding appropriate parameter sets for a given equation of state (EoS) to describe different properties of a certain substance is an optimization problem with...

parameter estimation | multi‐criteria optimization | pareto optimization | water | PC‐SAFT | PC-SAFT | multi-criteria optimization | MULTIOBJECTIVE OPTIMIZATION | RENORMALIZATION-GROUP CORRECTIONS | OF-STATE | LIQUID-EQUILIBRIUM | PHASE-EQUILIBRIUM | MOLECULAR-BASED EQUATIONS | DECISION-SUPPORT | ENGINEERING, CHEMICAL | PROCESS DESIGN | ASSOCIATING FLUID THEORY | PERTURBED-CHAIN-SAFT | Thermodynamics | Pareto efficiency | Analysis | Multiple criterion | Equations of state | Vapor pressure | Pareto optimization | Mathematical models | Thermodynamic properties | Parameterization | Optimization

parameter estimation | multi‐criteria optimization | pareto optimization | water | PC‐SAFT | PC-SAFT | multi-criteria optimization | MULTIOBJECTIVE OPTIMIZATION | RENORMALIZATION-GROUP CORRECTIONS | OF-STATE | LIQUID-EQUILIBRIUM | PHASE-EQUILIBRIUM | MOLECULAR-BASED EQUATIONS | DECISION-SUPPORT | ENGINEERING, CHEMICAL | PROCESS DESIGN | ASSOCIATING FLUID THEORY | PERTURBED-CHAIN-SAFT | Thermodynamics | Pareto efficiency | Analysis | Multiple criterion | Equations of state | Vapor pressure | Pareto optimization | Mathematical models | Thermodynamic properties | Parameterization | Optimization

Journal Article

Physics of Plasmas, ISSN 1070-664X, 05/2007, Volume 14, Issue 5, pp. 052110 - 052110-9

A nominally axisymmetric plasma configuration, such as a tokamak or a spherical torus, is highly sensitive to nonaxisymmetric magnetic perturbations due to...

RESISTIVE WALL MODES | PHYSICS, FLUIDS & PLASMAS | PERTURBED PLASMA EQUILIBRIA | PHYSICS | DIII-D | FEEDBACK | INSTABILITIES | AXIAL SYMMETRY | DISTURBANCES | PLASMA SIMULATION | CALCULATION METHODS | MAGNETOHYDRODYNAMICS | CURRENTS | THREE-DIMENSIONAL CALCULATIONS | SPHERICAL CONFIGURATION | TOKAMAK DEVICES | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY | PLASMA | EQUILIBRIUM | PLASMA CONFINEMENT

RESISTIVE WALL MODES | PHYSICS, FLUIDS & PLASMAS | PERTURBED PLASMA EQUILIBRIA | PHYSICS | DIII-D | FEEDBACK | INSTABILITIES | AXIAL SYMMETRY | DISTURBANCES | PLASMA SIMULATION | CALCULATION METHODS | MAGNETOHYDRODYNAMICS | CURRENTS | THREE-DIMENSIONAL CALCULATIONS | SPHERICAL CONFIGURATION | TOKAMAK DEVICES | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY | PLASMA | EQUILIBRIUM | PLASMA CONFINEMENT

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