• Title, Summary, Keyword: variational

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OPTIMALITY CRITERIA AND DUALITY FOR MULTIOBJECTIVE VARIATIONAL PROBLEMS INVOLVING HIGHER ORDER DERIVATIVES

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.123-137
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    • 2009
  • A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

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SYSTEM OF MIXED VARIATIONAL INEQUALITIES IN REFLEXIVE BANACH SPACES

  • Ahmad, Rais;Usman, Farhat
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.693-702
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    • 2009
  • In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.

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SYSTEM OF GENERALIZED NONLINEAR REGULARIZED NONCONVEX VARIATIONAL INEQUALITIES

  • Salahuddin, Salahuddin
    • Korean Journal of Mathematics
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    • v.24 no.2
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    • pp.181-198
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    • 2016
  • In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

EXISTENCE RESULTS FOR VECTOR NONLINEAR INEQUALITIES

  • Lee, Suk-Jin;Lee, Byung-Soo
    • Communications of the Korean Mathematical Society
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    • v.18 no.4
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    • pp.737-743
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    • 2003
  • The purpose of this paper is to consider some existence results for vector nonlinear inequalities without any monotonicity assumption. As consequences of our main result, we give some existence results for vector equilibrium problem, vector variational-like inequality problem and vector variational inequality problems as special cases.

GENERALIZED NONLINEAR MULTIVALUED MIXED QUASI-VARIATIONAL-LIKE INEQUALITIES

  • Lee, Byung-Soo;Khan M. Firdosh;Salahuddin Salahuddin
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.689-700
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    • 2006
  • In this paper, we introduce a new class of generalized nonlinear multivalued mixed quasi-variational-like inequalities and prove the existence and uniqueness of solutions for the class of generalized nonlinear multivalued mixed quasi-variational-like inequalities in reflexive Banach spaces using Fan-KKM Theorem.

A SYSTEM OF NONLINEAR SET-VALUED IMPLICIT VARIATIONAL INCLUSIONS IN REAL BANACH SPACES

  • Bai, Chuanzhi;Yang, Qing
    • Communications of the Korean Mathematical Society
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    • v.25 no.1
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    • pp.129-137
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    • 2010
  • In this paper, we introduce and study a system of nonlinear set-valued implicit variational inclusions (SNSIVI) with relaxed cocoercive mappings in real Banach spaces. By using resolvent operator technique for M-accretive mapping, we construct a new class of iterative algorithms for solving this class of system of set-valued implicit variational inclusions. The convergence of iterative algorithms is proved in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works.

GENERALIZED SET-VALVED STRONGLY NONLINEAR VARIATIONAL INEQUALITIES IN BANACH SPACES

  • Cho, Y.J.;Fang, Y.P.;Huang, N.J.;Kim, K.H.
    • Journal of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.195-205
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    • 2003
  • In this paper, we introduce and study a new class of generalized strongly nonlinear variational inequalities with setvalued mappings. By using the KKM technique, we prove the existence and uniqueness of solution for this class of generalized setvalued strongly nonlinear variational inequalities in reflexive Banach spaces. Our results include the main results of Verma [16], [17] as special cases.

ALGORITHMS FOR SYSTEMS OF NONLINEAR VARIATIONAL INEQUALITIES

  • Cho, Y.J.;Fang, Y.P.;Huang, N.J.;Hwang, H.J.
    • Journal of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.489-499
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    • 2004
  • In this paper, we introduce and study a new system of nonlinear variational inequalities. The existence and uniqueness of solution for this problem are proved and an iterative algorithm for approximating the solution of system of nonlinear variational inequalities is constructed.

VARIATIONAL PRINCIPLE FOR QUANTUM UNBOUNDED SPIN SYSTEMS

  • Choi, S.D.;Jo, S.G.;Kim, H.I.;Lee, H.H.;Yoo, H.J.
    • Journal of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.579-592
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    • 2000
  • We study the variational principle for quantum unbounded spin systems interacting via superstable and regular interactions. We show that the (weak) KMS state constructed via the thermodynamic limit of finite volume Green's functions satisfies the Gibbs variational equality.

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A PARALLEL HYBRID METHOD FOR EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITIES AND NONEXPANSIVE MAPPINGS IN HILBERT SPACE

  • Hieu, Dang Van
    • Journal of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.373-388
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    • 2015
  • In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.