Mathematical Programming

, Volume 75, Issue 3, pp 441–465 | Cite as

Solvability theory for a class of hemivariational inequalities involving copositive plus matrices applications in robotics

  • D. Goeleven
  • G. E. Stavroulakis
  • P. D. Panagiotopoulos


The study of the equilibrium of an object-robotic hand system including nonmonotone adhesive effects and nonclassical friction effects leads to new inequality methods in robotics. The aim of this paper is to describe these inequality methods and provide a corresponding suitable mathematical theory.


Hemivariational Inequality Copositive Plus Matrix Unilateral Contact in Mechanics Robotics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Adly, D. Goeleven and M. Théra, “Recession mappings and noncoercive variational inequalities,” to appear inNonlinear Analysis: Theory, Methods and Applications.Google Scholar
  2. [2]
    A.M. Al-Fahed, G.E. Stavroulakis and P.D. Panagiotopoulos, A linear complementarity approach to the frictionless gripper,”The International Journal of Robotic Research 11(2) (1992) 112–122.CrossRefGoogle Scholar
  3. [3]
    J.P. Aubin and H. Frankowska,Set-valued Analysis (Birkhäuser, Basel, Boston, 1990).MATHGoogle Scholar
  4. [4]
    H. Brézis, “Equations et inéquations non linéaires dans les espaces vectoriels en dualité,”Annales de l' Institut Fourier, Grenoble 18 (1968) 115–175.MATHGoogle Scholar
  5. [5]
    F.E. Browder and P. Hess, “Nonlinear mappings of monotone type in Banach spaces,”Journal of Functional Analysis 11 (1972) 251–294.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    F.E Browder,Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces Proceedings of Symposia in Pure Mathematics, Vol. XVIII, Part 2 (American Mathematical Society, Providence, Rhode Island, 1976).MATHGoogle Scholar
  7. [7]
    F.H. Clarke,Nonsmooth Analysis and Optimization (Wiley, New York 1984).Google Scholar
  8. [8]
    G. Duvaut and J.L. Lions,Les Inéquations en Mécanique, et en Physique (Dunod, Paris, 1972).MATHGoogle Scholar
  9. [9]
    G. Fichera, “The Signorini elastostatics problem with ambiguous boundary conditions,” in:Proceedings of the International Conference on the Application of the Theory of Functions in Continuum Mechanics I (Tbilisi, 1963).Google Scholar
  10. [10]
    G. Fichera, “Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno,”Rendiconti del Academia Nazionale dei Lincei (VIII) 7 (1964) 91–114.MathSciNetGoogle Scholar
  11. [11]
    G. Fichera, “Existence theorems in elasticity,” in: S. Flügge, ed,Encyclopedia of Physics, VIa.2 (Springer, Berlin, 1972) pp. 347–389.Google Scholar
  12. [12]
    G. Fichera, “Boundary value problems in elasticity with unilateral constraints,” in: S. Flügge, ed.Encyclopedia of Physics, VIa.2 (Springer, Berlin, 1972) pp. 391–424.Google Scholar
  13. [13]
    D. Goeleven, “On the solvability of noncoercive linear variational inequalities in separable Hilbert spaces,”Journal of Optimization Theory and Applications 79(3) (1993) 493–511.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    D. Goeleven, “On noncoercive variational inequalities, and some appications in unilateral mechanics,” Ph.D. dissertation, Department of Mathematics, FUNDP, Namur, Belgium, 1993.Google Scholar
  15. [15]
    D. Goeleven, “Noncoercive hemivariational inequality and its applications in nonconvex unilateral mechanics,”Applications of Mathematics 41 (1996) 203–229.MATHMathSciNetGoogle Scholar
  16. [16]
    D. Goeleven, “Noncoercive variational problems and related results,” to appear in: Pitman Research Notes in Mathematics Series, Longman.Google Scholar
  17. [17]
    M.S. Gowda and T.I. Seidman, “Generalized linear complementarity problems,”Mathematical Programming 46 (1990) 329–340.MATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    C.E. Lemke, “Bimatrix equilibrium points and mathematical programming,”Management Science 11 (1965) 681–689.MathSciNetCrossRefGoogle Scholar
  19. [19]
    G. Maier, “Incremental plastic analysis in the presence of large displacements and physical instabilizing,”International Journal of Solids Structures 7 (1971) 345–372.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    J.J. Moreau, “La notion de sur-potentiel et les liaisons unilatérales en élastostatique,”Comptes Rendus de l'Académie des Sciences de Paris 267A (1968) 954–957.MathSciNetGoogle Scholar
  21. [21]
    J.J. Moreau and P.D. Panagiotopoulos (eds),Nonsmooth Mechanics and Applications, CISM Vol. 302 (Springer, New York, Wien, 1988).MATHGoogle Scholar
  22. [22]
    Z. Naniewicz, “On the pseudo-monotonicity of generalized gradients of nonconvex functions,”Applicable Analysis 47 (1992) 151–172.MATHMathSciNetGoogle Scholar
  23. [23]
    Z. Naniewicz, “Hemivariational inequality approach to constrained problems for star-shaped admissible sets,”Journal of Optimization Theory and Applications 83(1) (1994) 97–112.MATHCrossRefMathSciNetGoogle Scholar
  24. [24]
    Z. Naniewicz and P.D. Panagiotopoulos,The Mathematical Theory of Hemivariational Inequalities and Applications (Marcel Dekker, New York, 1995).Google Scholar
  25. [25]
    P.D. Panagiotopoulos,Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions (Birkhäuser, Basel, 1985).MATHGoogle Scholar
  26. [26]
    P.D. Panagiotopoulos,Hemivariational Inequalities. Applications in Mechanics and Engineering (Springer, Berlin, Heidelberg, 1993).MATHGoogle Scholar
  27. [27]
    P.D. Panagiotopoulos and A.M. Al-Fahed, “Robot hand grasping and related problems: Optimal control and identification,”The International Journal of Robotics Research 13(2) (1994) 127–136.CrossRefGoogle Scholar
  28. [28]
    J.S. Pang, J.C. Trinkle and G. Lo, “A complementarity approach to a quasistatic rigid body motion problem,” manuscript, Department of Mathematical Sciences, The Johns Hopkins University, (Baltimore, MD, 1993).Google Scholar
  29. [29]
    J.S. Pang and J.C. Trinkle, “Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction”, to appear inMathematical Programming.Google Scholar
  30. [30]
    G.E. Stavroulakis, P.D. Panagiotopoulos and A.M. Al-Fahed, “On the rigid body displacements and rotations in unilateral contact problems and applications,”Computer and Structures 40(3) (1991) 599–614.MATHCrossRefGoogle Scholar

Copyright information

© Elsevier Science B. V 1996

Authors and Affiliations

  • D. Goeleven
    • 1
  • G. E. Stavroulakis
    • 2
  • P. D. Panagiotopoulos
    • 3
    • 4
  1. 1.Chargé de Recherches FNRS, Department of MathematicsFacultés Universitaires N-D de la PaixNamurBelgium
  2. 2.Department of Engineering SciencesTechnical University of CreteChaniaGreece
  3. 3.Aristotle University, School of TechnologyChair of Steel StructuresThessalonikiGreece
  4. 4.Institute for Technical Mechanics, Faculty of Mathematics and PhysicsRWTH AachenAachenGermany

Personalised recommendations