A general minimax inequality and its consequences

Authors: Sebestyén, Zoltán

Source: Publicationes Mathematicae Debrecen. 35:115-118

Subject Terms: Optimality conditions for minimax problems, finite intersection property, Existence theories for problems in abstract spaces, Existence of solutions for minimax problems, 0101 mathematics, general minimax theorem, 01 natural sciences

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Access URL: https://zbmath.org/4063884

Viability for locally monotone evolution inclusions and lower semicontinuous solutions of Hamilton–Jacobi–Bellman equations in infinite dimensions: Viability for locally monotone evolution inclusions and lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations in infinite dimensions

Authors: Jichao Jiang, Christian Keller

Source: ESAIM: Control, Optimisation and Calculus of Variations. 31:4

Subject Terms: viscosity solution, 0209 industrial biotechnology, locally monotone operator, Evolution inclusions, heat equation, Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games, viability, path-dependent partial differential equation, 02 engineering and technology, Hamilton-Jacobi equation, 01 natural sciences, contingent solution, optimal control, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), FOS: Mathematics, Existence theories for problems in abstract spaces, Nonlinear evolution equations, 0101 mathematics, Monotone operators and generalizations, evolution inclusion, Mathematics - Optimization and Control, 34G25, 47H05, 47J35, 49L25, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2408.02915

On the structural representation of S-homogenized optimal control problems: On the structural representation of \(S\)-homogenized optimal control problems

Authors: Kogut, P.I.

Subject Terms: Methods involving semicontinuity and convergence, relaxation, optimal control problem, homogenization, \(S\)-convergence, Existence theories for problems in abstract spaces, Homogenization in context of PDEs, PDEs in media with periodic structure

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Access URL: https://zbmath.org/1641375
http://dspace.nbuv.gov.ua/handle/123456789/169276

ITERATIVE ALGORITHMS FOR DATA ASSIMILATION PROBLEMS: Iterative algorithms for data assimilation problems

Authors: Victor P. Shutyaev, Guriĭ Ivanovich Marchuk

Source: Frontiers in Mathematical Analysis and Numerical Methods ISBN: 9789812389411

Subject Terms: Numerical optimization and variational techniques, convergence, Discrete approximations in optimal control, iterative algorithms, minimization of functionals, Hilbert space, 01 natural sciences, constrained minimum problem, optimal control, boundary value problem, data assimilation problems, Existence theories for problems in abstract spaces, 0101 mathematics, 0105 earth and related environmental sciences

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Access URL: https://zbmath.org/1799640
https://doi.org/10.1142/s0252959902000225
https://www.worldscientific.com/doi/abs/10.1142/S0252959902000225

Evolution hemivariational inequalities in infinite dimension and their control: Evolution hemivariational inequalities in infinite dimension and their control.

Authors: Migórski, Stanisław

Source: Nonlinear Analysis: Theory, Methods & Applications. 47:101-112

Subject Terms: pseudomonotone operator, Evolution inclusions, selection, subdifferential, semicontinuity, evolution triple, hemivariational, parabolic, Variational inequalities, 01 natural sciences, hyperbolic, control problem, multifunction, Variational and other types of inequalities involving nonlinear operators (general), compact embedding, Existence theories for problems in abstract spaces, nonconvex function, 0101 mathematics

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https://www.sciencedirect.com/science/article/pii/S0362546X01001602
https://ruj.uj.edu.pl/xmlui/handle/item/80289

On Characterization of Solution Sets of Set-Valued Pseudoinvex Optimization Problems: On characterization of solution sets of set-valued pseudoinvex optimization problems

Authors: Jafar Zafarani, M. Oveisiha

Source: Journal of Optimization Theory and Applications. 163:387-398

Subject Terms: Programming in abstract spaces, set-valued map, 13. Climate action, 0211 other engineering and technologies, Stampaccia variational-like inequality, Existence theories for problems in abstract spaces, normal subdifferential, 02 engineering and technology, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Multi-objective and goal programming, solution set

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Access URL: https://zbmath.org/6380436
https://doi.org/10.1007/s10957-013-0509-z
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https://link.springer.com/article/10.1007/s10957-013-0509-z

Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems

Authors: Alexander J. Zaslavski

Source: Annales de l'Institut Henri Poincaré C, Analyse non linéaire. 22:579-596

Subject Terms: Lavrentiev phenomenon, Methods involving semicontinuity and convergence, relaxation, approximation in energy, Existence theories for free problems in one independent variable, Existence theories for problems in abstract spaces, 0101 mathematics, 01 natural sciences, Banach-valued functions, Mathematical Physics, Analysis

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https://eudml.org/doc/78670
http://ui.adsabs.harvard.edu/abs/2005AIHPC..22..579Z/abstract

Linking in Hilbert space

Authors: Kyril Tintarev, Martin Schechter

Source: Proceedings of the American Mathematical Society. 134:403-410

Subject Terms: Variational methods involving nonlinear operators, Nonlinear boundary value problems for linear elliptic equations, 0211 other engineering and technologies, Existence theories for problems in abstract spaces, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Critical point theory, variational methods, saddle point theory

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https://zbmath.org/2227180
https://doi.org/10.1090/s0002-9939-05-08217-1
https://www.ams.org/proc/2006-134-02/S0002-9939-05-08217-1/S0002-9939-05-08217-1.pdf
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https://www.ams.org/journals/proc/2006-134-02/S0002-9939-05-08217-1/home.html

Existence of two local minima for functionals on reflexive Banach spaces

Authors: ANELLO, Giovanni

Source: Nonlinear Analysis: Theory, Methods & Applications. 61:1179-1187

Subject Terms: reflexive spaces, Nonlinear boundary value problems for ordinary differential equations, Variational methods involving nonlinear operators, critical points, variational methods, Existence theories for problems in abstract spaces, 0101 mathematics, local minima, 01 natural sciences, Set-valued and variational analysis

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https://doi.org/10.1016/j.na.2005.01.096
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https://www.sciencedirect.com/science/article/pii/S0362546X05001380#!
https://hdl.handle.net/11570/1890190

Slice-continuous sets in reflexive Banach spaces: convex constrained optimization and strict convex separation

Authors: Constantin Zălinescu, Emil Ernst, Michel Théra

Source: Journal of Functional Analysis. 223:179-203

Subject Terms: Slice-continuous set, Well-positioned set, Asymptote, Convex programming, strict convex separation, slice-continuous set, Stability, separation, extension, and related topics for functional equations, Continuous set, well-positioned set, 01 natural sciences, constrained optimization, Strict convex separation, Convex functions and convex programs in convex geometry, asymptote, continuous set, Existence theories for problems in abstract spaces, 0101 mathematics, Constrained optimization, Monotone operators and generalizations, Analysis

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https://core.ac.uk/display/82347040

Iterative algorithm of solutions for generalized mixed implicit equilibrium-like problems

Authors: Xie Ping Ding

Source: Applied Mathematics and Computation. 162:799-809

Subject Terms: Numerical optimization and variational techniques, generalized mixed implicit equilibrium-like problem, algorithm, partially relaxed monotonicity, auxiliary problem principle, Hilbert space, 0211 other engineering and technologies, Existence theories for problems in abstract spaces, 02 engineering and technology, predictor-corrector iterative algorithms, 0101 mathematics, Variational inequalities, 01 natural sciences

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Access URL: https://dblp.uni-trier.de/db/journals/amc/amc162.html#Ding05
https://www.sciencedirect.com/science/article/pii/S0096300304001328

On the fundamental state energy for a Schrödinger operator with magnetic field in domains with corners

Authors: Bonnaillie, Virginie

Source: Asymptotic Analysis. 41:215-258

Subject Terms: Ginzburg-Landau's functional, asymptotic behavior of the energy, fundamental state for the Schrödinger operator, NLS equations (nonlinear Schrödinger equations), Applications of variational problems in infinite-dimensional spaces to the sciences, Hessian, asymptotics of the smallest eigenvalue, Estimates of eigenvalues in context of PDEs, Existence theories for problems in abstract spaces, eigenfunctions, simply connected domain with Lipschitzian boundary, Statistical mechanics of superconductors

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Access URL: https://zbmath.org/2162733

Generic solutions for some perturbed optimization problem in non-reflexive Banach spaces

Authors: Renxing Ni

Source: Journal of Mathematical Analysis and Applications. 302:417-424

Subject Terms: Methods involving semicontinuity and convergence, relaxation, Applications of functional analysis in optimization, convex analysis, mathematical programming, economics, Applied Mathematics, Lower semicontinuous function, generic existence, 01 natural sciences, Boundedly relatively weakly compact subset, Perturbed optimization problems, well-posed problems, Existence theories for problems in abstract spaces, Sensitivity, stability, well-posedness, 0101 mathematics, Dense Gδ-subset, best approximation, perturbed problems, Analysis

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Access URL: https://zbmath.org/2136656
https://doi.org/10.1016/j.jmaa.2004.03.069
https://core.ac.uk/display/82493523
https://www.sciencedirect.com/science/article/pii/S0022247X04002021
http://ui.adsabs.harvard.edu/abs/2005JMAA..302..417N/abstract

Existence of efficient solutions in infinite horizon optimization under continuous and discrete controls

Authors: Robert L. Smith, Irwin E. Schochetman

Source: Operations Research Letters. 33:97-104

Subject Terms: optimal control, Management decision making, including multiple objectives, Discrete-time control/observation systems, production planning, 0502 economics and business, 05 social sciences, 0211 other engineering and technologies, Existence theories for problems in abstract spaces, 02 engineering and technology, efficient solutions

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Access URL: https://zbmath.org/2116857
https://doi.org/10.1016/j.orl.2004.04.005

Characterizations of p-superharmonic functions on metric spaces: Characterizations of \(p\)-superharmonic functions on metric spaces

Authors: Anders Björn

Source: Studia Mathematica. 169:45-62

Subject Terms: Harmonic, subharmonic, superharmonic functions on other spaces, \(p\)-harmonic function, Poincaré inequality, superminimizer, doubling measure, Existence theories for problems in abstract spaces, Nonlinear elliptic equations, 0101 mathematics, 01 natural sciences, Dirichlet \(p\)-regular open sets, \(p\)-superhamonicity, Other generalizations (nonlinear potential theory, etc.)

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https://zbmath.org/2159576
https://doi.org/10.4064/sm169-1-3
https://dialnet.unirioja.es/servlet/articulo?codigo=1155122
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https://eudml.org/doc/285288
http://journals.impan.pl/cgi-bin/doi?sm169-1-3

On a class of nonconvex equilibrium problems

Authors: Muhammad Aslam Noor

Source: Applied Mathematics and Computation. 157:653-666

Subject Terms: Numerical optimization and variational techniques, convergence, iterative algorithms, equilibrium problems, auxiliary problem principle, Hilbert space, Minty lemma, Existence theories for problems in abstract spaces, 0101 mathematics, Variational inequalities, 01 natural sciences, variational inequalities

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Access URL: https://www.sciencedirect.com/science/article/pii/S0096300303009615
http://dblp.uni-trier.de/db/journals/amc/amc157.html#Noor04

Compactness via symmetrization

Authors: Almut Burchard, Yan Guo

Source: Journal of Functional Analysis. 214:40-73

Subject Terms: Variational methods for second-order elliptic equations, Concentration compactness, Methods involving semicontinuity and convergence, relaxation, Euler-Poisson system, Symmetric rearrangement, Hardy-Littlewood-Sobolev inequality, Sobolev inequality, 16. Peace & justice, 01 natural sciences, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Dynamical stability, dynamic stability, symmetric rearrangement, Existence theories for problems in abstract spaces, Vlasov-Poisson system, concentration compactness, stellar dynamics, 0101 mathematics, Stellar dynamics, Analysis

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Access URL: https://zbmath.org/2107266
https://doi.org/10.1016/j.jfa.2004.04.005
http://www.sciencedirect.com/science/article/pii/S0022123604001247
https://www.math.toronto.edu/almut/preprints/BurchardGuo2.pdf
https://core.ac.uk/display/82607074
https://www.sciencedirect.com/science/article/pii/S0022123604001247

Linear-Quadratic Discrete Optimal Control Problems for Descriptor Systems in Hilbert Space: Linear-quadratic discrete optimal control problems for descriptor systems in Hilbert space

Authors: G. A. Kurina

Source: Journal of Dynamical and Control Systems. 10:365-375

Subject Terms: optimal control, 0209 industrial biotechnology, Discrete-time control/observation systems, linear-quadratic problems, Linear-quadratic optimal control problems, Existence theories for problems in abstract spaces, 02 engineering and technology, discrete descriptor systems

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Access URL: https://zbmath.org/2091632
https://doi.org/10.1023/b:jods.0000034435.80761.32
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Strongly nonlinear impulsive evolution equations and optimal control

Authors: Pairote, Sattayatham

Source: Nonlinear Analysis: Theory, Methods & Applications. 57:1005-1020

Subject Terms: Evolution triple, Nonlinear impulsive evolution equations, nonlinear impulsive evolution equations, Nonlinear differential equations in abstract spaces, Ordinary differential equations with impulses, 01 natural sciences, optimal control, Existence theories for optimal control problems involving ordinary differential equations, Nonlinear monotone operator, Impulsive optimal control problems, Existence theories for problems in abstract spaces, Control/observation systems in abstract spaces, control of impulsive evolution equations, 0101 mathematics, Lagrange problems

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http://sutir.sut.ac.th:8080/jspui/bitstream/123456789/663/2/Strongly%20nonlinear%20impulsive%20evolution%20equations%20and%20optimal%20control%20_OTOP_full.pdf
https://www.sciencedirect.com/science/article/pii/S0362546X04000963
http://sutir.sut.ac.th:8080/sutir/handle/123456789/663
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A Solution Algorithm for Problems of Optimal Control in Hilberts Space: A solution algorithm for problems of optimal control in Hilbert spaces

Authors: V. I. Maksimov, A. V. Kryazhimskii

Source: Journal of Mathematical Sciences. 121:2226-2247

Subject Terms: optimal control, 0209 industrial biotechnology, iterative algorithm, convergence, Other numerical methods in calculus of variations, 0103 physical sciences, Existence theories for problems in abstract spaces, 02 engineering and technology, 01 natural sciences

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https://doi.org/10.1023/b:joth.0000023088.97567.00
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