Engineering and Economic Applications of Complementarity Problems

This paper gives an extensive documentation of applications of finite-dimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.

[1]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[3]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[4]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[5]  L. Walras Elements of Pure Economics , 1954 .

[6]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[7]  Steven Vajda,et al.  The Theory of Linear Economic Models , 1960 .

[8]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[9]  Richaard W. Cottle Nonlinear Programs with Positively Bounded Jacobians , 1966 .

[10]  G. Maier A quadratic programming approach for certain classes of non linear structural problems , 1968 .

[11]  G. Maier A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .

[12]  G. Dantzig,et al.  A generalization of the linear complementarity problem , 1970 .

[13]  A. Seireg,et al.  A Mathematical Programming Method for Design of Elastic Bodies in Contact , 1971 .

[14]  G. Maier Incremental plastic analysis in the presence of large displacements and physical instabilizing effects , 1971 .

[15]  C. Cryer The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences , 1971 .

[16]  Giulio Maier,et al.  Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity , 1972 .

[17]  G. Maier,et al.  Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity , 1972 .

[18]  T. Koopmans,et al.  On the definition and computation of a capital stock invariant under optimization , 1972 .

[19]  Francesco Mallegni,et al.  The Computation of Economic Equilibria , 1973 .

[20]  Herbert E. Scarf,et al.  The Computation of Economic Equilibria , 1974 .

[21]  Peter A. Steenbrink,et al.  Optimization of Transport Networks , 1974 .

[22]  G. Dantzig,et al.  A complementarity algorithm for an optimal capital path with invariant proportions , 1974 .

[23]  Larry J. LeBlanc,et al.  AN EFFICIENT APPROACH TO SOLVING THE ROAD NETWORK EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM. IN: THE AUTOMOBILE , 1975 .

[24]  O. Mangasarian Equivalence of the Complementarity Problem to a System of Nonlinear Equations , 1976 .

[25]  M. Todd The Computation of Fixed Points and Applications , 1976 .

[26]  Michael Florian,et al.  Traffic Equilibrium Methods , 1976 .

[27]  R. S. Sacher,et al.  On the solution of large, structured linear complementarity problems: The block partitioned case , 1977 .

[28]  Ikuyo Kaneko A mathematical programming method for the inelastic analysis of reinforced concrete frames , 1977 .

[29]  丸山 徹 Convex Analysisの二,三の進展について , 1977 .

[30]  R. Cottle,et al.  A SPECIAL CLASS OF LARGE QUADRATIC PROGRAMS , 1978 .

[31]  I. Adelman,et al.  Income distribution policy in developing countries , 1978 .

[32]  M. Kostreva,et al.  On a Direct Algorithm for Nonlinear Complementarity Problems , 1978 .

[33]  Ikuyo Kaneko Piecewise linear elastic–plastic analysis , 1979 .

[34]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[35]  N. Josephy Newton's Method for Generalized Equations. , 1979 .

[36]  Ray Robinson Taxation and Subsidies , 1979 .

[37]  Ikuyo Kaneko Complete solutions for a class of elastic-plastic structures , 1980 .

[38]  V. Ginsburgh,et al.  Activity analysis and general equilibrium modelling , 1981 .

[39]  Per Lötstedt Coulomb Friction in Two-Dimensional Rigid Body Systems , 1981 .

[40]  K. Derviş,et al.  General equilibrium models for development policy , 1982 .

[41]  Hanif D. Sherali,et al.  A mathematical programming approach for determining oligopolistic market equilibrium , 1982, Math. Program..

[42]  J. S. Pang,et al.  The Generalized Quasi-Variational Inequality Problem , 1982, Math. Oper. Res..

[43]  Per Lötstedt Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints , 1982 .

[44]  Tony E. Smith,et al.  A NONLINEAR COMPLEMENTARITY FORMULATION AND SOLUTION PROCEDURE FOR THE GENERAL DERIVED DEMAND NETWORK EQUILIBRIUM PROBLEM , 1983 .

[45]  R. Kellogg,et al.  Pathways to solutions, fixed points, and equilibria , 1983 .

[46]  Hanif D. Sherali,et al.  Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations , 1983, Oper. Res..

[47]  J. Shoven,et al.  Applied General Equilibrium Models of Taxation and International Trade , 1983 .

[48]  M. Kostreva Elasto-hydrodynamic lubrication: A non-linear complementarity problem , 1984 .

[49]  P. Petri Modeling Japanese-American Trade: A Study of Asymmetric Interdependence , 1984 .

[50]  T. Magnanti MODELS AND ALGORITHMS FOR PREDICTING URBAN TRAFFIC EQUILIBRIA , 1984 .

[51]  K. P. Oh Analysis of a Needle Bearing , 1984 .

[52]  Rs Stainton,et al.  Pathways to solutions , 1984 .

[53]  Jong-Shi Pang,et al.  Linearized simplicial decomposition methods for computing traffic equilibria on networks , 1984, Networks.

[54]  K. P. Oh The Numerical Solution of Dynamically Loaded Elastohydrodynamic Contact as a Nonlinear Complementarity Problem , 1984 .

[55]  Roberto Contro,et al.  Optimal design of beams discretized by elastic plastic finite element , 1985 .

[56]  Alain Haurie,et al.  On the relationship between Nash - Cournot and Wardrop equilibria , 1983, Networks.

[57]  P. K. Goenka,et al.  The Elastohydrodynamic Solution of Journal Bearings Under Dynamic Loading , 1985 .

[58]  P. Panagiotopoulos Inequality problems in mechanics and applications , 1985 .

[59]  John Whalley,et al.  A General Equilibrium Model for Tax Policy Evaluation , 1985 .

[60]  Terry L. Friesz,et al.  TRANSPORTATION NETWORK EQUILIBRIUM, DESIGN AND AGGREGATION: KEY DEVELOPMENTS AND RESEARCH OPPORTUNITIES. IN: THE AUTOMOBILE , 1985 .

[61]  R. Rockafellar,et al.  A Lagrangian Finite Generation Technique for Solving Linear-Quadratic Problems in Stochastic Programming , 1986 .

[62]  A. Klarbring A mathematical programming approach to three-dimensional contact problems with friction , 1986 .

[63]  K. P. Oh The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem , 1986 .

[64]  Patrice Marcotte,et al.  Network design problem with congestion effects: A case of bilevel programming , 1983, Math. Program..

[65]  Michael Florian,et al.  Nonlinear cost network models in transportation analysis , 1986 .

[66]  A. Klarbring Quadratic programs in frictionless contact problems , 1986 .

[67]  Roger J.-B. Wets,et al.  Linear-quadratic programming problems with stochastic penalties: The finite generation algorithm , 1986 .

[68]  Patrick T. Harker,et al.  Alternative Models of Spatial Competition , 1986, Oper. Res..

[69]  Claudia Starr,et al.  General Equilibrium Trade Policy Modelling , 1987 .

[70]  J. Haaland VEMOD: A Ricardo-Heckscher-Ohlin-Jones Model of World Trade , 1987 .

[71]  V. T. Rajan,et al.  Dynamics of a rigid body in frictional contact with rigid walls: Motion in two dimensions , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[72]  K. P. Oh,et al.  Elastohydrodynamic Lubrication of Piston Skirts , 1987 .

[73]  R. Rockafellar Linear-quadratic programming and optimal control , 1987 .

[74]  Lars Mathiesen,et al.  An algorithm based on a sequence of linear complementarity problems applied to a walrasian equilibrium model: An example , 1987, Math. Program..

[75]  Thomas Rutherford,et al.  A Modeling System for Applied General Equilibrium Analysis , 1987 .

[76]  T. Srinivasan,et al.  General Equilibrium Trade Policy Modeling. , 1987 .

[77]  J. A. Ventura,et al.  Restricted simplicial decomposition: computation and extensions , 1987 .

[78]  J. Rodrigues Obstacle Problems in Mathematical Physics , 1987 .

[79]  A. Klarbring On discrete and discretized non-linear elastic structures in unilateral contact (stability, uniqueness and variational principles) , 1988 .

[80]  A. Klarbring,et al.  A mathematical programming approach to contact problems with friction and varying contact surface , 1988 .

[81]  J. Pang,et al.  Existence of optimal solutions to mathematical programs with equilibrium constraints , 1988 .

[82]  B. Kwak,et al.  A complementarity problem formulation for two-dimensional frictional contact problems , 1988 .

[83]  Roger L. Tobin A variable dimension solution approach for the general spatial price equilibrium problem , 1988, Math. Program..

[84]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[85]  Shinji Mizuno,et al.  A new continuation method for complementarity problems with uniformP-functions , 1989, Math. Program..

[86]  J. Markusen,et al.  Nash Equilibrium Tariffs for the United States and Canada: The Roles of Country Size, Scale Economies, and Capital Mobility , 1989, Journal of Political Economy.

[87]  R. Hoppe,et al.  A multi-grid continuation strategy for parameter-dependent variational inequalities , 1989 .

[88]  G. Maier,et al.  Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening , 1989 .

[89]  E. Miersemann,et al.  Continuation for parametrized nonlinear variational inequalities , 1989 .

[90]  Patrick T. Harker,et al.  Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach , 1990, Math. Program..

[91]  R. Rockafellar,et al.  Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time , 1990 .

[92]  M. Kostreva Recent Results On Complementarity Models For Engineering And Economics , 1990 .

[93]  W. DeSarbo,et al.  Product Positioning Under Price Competition , 1990 .

[94]  Jirí Vladimír Outrata,et al.  On the numerical solution of a class of Stackelberg problems , 1990, ZOR Methods Model. Oper. Res..

[95]  R. Tyrrell Rockafellar,et al.  Computational schemes for large-scale problems in extended linear-quadratic programming , 1990, Math. Program..

[96]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[97]  F. Tin-Loi,et al.  Large scale nonholonomic elastoplastic analysis using a linear complementary formulation , 1990 .

[98]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[99]  Jong-Shi Pang,et al.  A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems , 1991, Math. Program..

[100]  F. Tin-Loi,et al.  Large displacement elastoplastic analysis of frames using an iterative LCP approach , 1991 .

[101]  Nimrod Megiddo,et al.  Homotopy Continuation Methods for Nonlinear Complementarity Problems , 1991, Math. Oper. Res..

[102]  D. C. Sun A Thermal Elastica Theory of Piston-Ring and Cylinder-Bore Contact , 1991 .

[103]  P. Panagiotopoulos,et al.  On the rigid body displacements and rotations in unilateral contact problems and applications , 1991 .

[104]  G. Isac,et al.  The generalized order complementarity problem , 1991 .

[105]  Nimrod Megiddo,et al.  A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems , 1991, Lecture Notes in Computer Science.

[106]  B. Kwak Complementarity problem formulation of three-dimensional frictional contact , 1991 .

[107]  P. Panagiotopoulos,et al.  Hard and Soft Fingered Robot Grippers. The Linear Complementarity Approach , 1991 .

[108]  Gerardo Toraldo,et al.  On the Solution of Large Quadratic Programming Problems with Bound Constraints , 1991, SIAM J. Optim..

[109]  G. Björkman THE SOLUTION OF LARGE DISPLACEMENT FRICTIONLESS CONTACT PROBLEMS USING A SEQUENCE OF LINEAR COMPLEMENTARITY PROBLEMS , 1991 .

[110]  L. Johansson,et al.  The Rigid Punch Problem with Friction Using Variational Inequalities and Linear Complementarity , 1992 .

[111]  M. Kostreva,et al.  Global solvability of generalized linear complementarity problems and a related class of polynomial complementarity problems , 1992 .

[112]  Ciyou Zhu,et al.  Modified proximal point algorithm for extended linear-quadratic programming , 1992, Comput. Optim. Appl..

[113]  Jong-Shi Pang,et al.  An inexact NE/SQP method for solving the nonlinear complementarity problem , 1992, Comput. Optim. Appl..

[114]  Masao Fukushima,et al.  Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems , 1992, Math. Program..

[115]  G. Björkman Path following and critical points for contact problems , 1992 .

[116]  Friedrich Pfeiffer,et al.  Dynamics Of Assembly Processes With A Manipulator , 1992, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems.

[117]  Roger L. Tobin Uniqueness results and algorithm for Stackelberg-Cournot-Nash equilibria , 1992, Ann. Oper. Res..

[118]  P. Panagiotopoulos,et al.  A Linear Complementarity Approach to the Frictionless Gripper Problem , 1992 .

[119]  A. Klarbring,et al.  Solution of large displacement contact problems with friction using Newton's method for generalized equations , 1992 .

[120]  S. Yau,et al.  Obstacle problem for von Kármán equations , 1992 .

[121]  J. Outrata Necessary optimality conditions for Stackelberg problems , 1993 .

[122]  David G. Tarr,et al.  Trade Reform in the Partially Liberalized Economy of Turkey , 1993 .

[123]  F. A. Karnes,et al.  Pathways to Solutions , 1993 .

[124]  T. Rutherford,et al.  International Trade in Carbon Emission Rights and Basic Materials: General Equilibrium Calculations for 2020 , 1993 .

[125]  Jong-Shi Pang,et al.  Nonsmooth Equations: Motivation and Algorithms , 1993, SIAM J. Optim..

[126]  S. Meyn,et al.  THE EXISTENCE OF AN “I” , 2020, The Nature of Order, Book 4: The Luminous Ground.

[127]  J. Pang,et al.  Elastoplastic analysis of structures with nonlinear hardening: A nonlinear complementarity approach , 1993 .

[128]  R. Tyrrell Rockafellar,et al.  Primal-Dual Projected Gradient Algorithms for Extended Linear-Quadratic Programming , 1993, SIAM J. Optim..

[129]  Olvi L. Mangasarian,et al.  Nonlinear complementarity as unconstrained and constrained minimization , 1993, Math. Program..

[130]  H. Rodrigues A mixed variational formulation for shape optimization of solids with contact conditions , 1993 .

[131]  Jong-Shi Pang,et al.  NE/SQP: A robust algorithm for the nonlinear complementarity problem , 1993, Math. Program..

[132]  Osman Güler,et al.  Existence of Interior Points and Interior Paths in Nonlinear Monotone Complementarity Problems , 1993, Math. Oper. Res..

[133]  K. C. Park,et al.  A computational procedure for flexible beams with frictional contact constraints , 1993 .

[134]  A. Auslender Convergence of stationary sequences for variational inequalities with maximal monotone operators , 1993 .

[135]  D. Jorgenson,et al.  Reducing US carbon emissions: an econometric general equilibrium assessment , 1993 .

[136]  Ahmad M. Al-Fahed Nuseirat,et al.  Robot Hand Grasping and Related Problems: Optimal Control and Identification , 1994, Int. J. Robotics Res..

[137]  A. S. Manne,et al.  International Trade in Oil, Gas and Carbon Emission Rights: An Intertemporal General Equilibrium Model* , 1994 .

[138]  Daniel Ralph,et al.  Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search , 1994, Math. Oper. Res..

[139]  S. Dirkse Robust solution of mixed complementary problems , 1994 .

[140]  Patrick T. Harker,et al.  A nonsmooth Newton method for variational inequalities, II: Numerical results , 1994, Math. Program..

[141]  Michael C. Ferris,et al.  The GAMS Callable Program Library for Variational and Complementarity Solvers , 1994 .

[142]  Patrick T. Harker,et al.  A nonsmooth Newton method for variational inequalities, I: Theory , 1994, Math. Program..

[143]  R. Sznajder,et al.  The Generalized Order Linear Complementarity Problem , 1994, SIAM J. Matrix Anal. Appl..

[144]  Masakazu Kojima,et al.  Global convergence in infeasible-interior-point algorithms , 1994, Math. Program..

[145]  Takayuki Arai,et al.  Numerical Simulation of Piston Ring in Mixed Lubrication—A Nonaxisymmetrical Analysis , 1994 .

[146]  C. Kanzow Some equation-based methods for the nonlinear complementarity problem , 1994 .

[147]  David Baraff,et al.  Fast contact force computation for nonpenetrating rigid bodies , 1994, SIGGRAPH.

[148]  J. Pang,et al.  A Trust Region Method for Constrained Nonsmooth Equations , 1994 .

[149]  Seok-Soon Lee A computational method for frictional contact problem using finite element method , 1994 .

[150]  T. Rutherford,et al.  Complementarity and increasing returns in intermediate inputs , 1994 .

[151]  S. M. Robinson Newton's method for a class of nonsmooth functions , 1994 .

[152]  T. Rutherford Extension of GAMS for complementarity problems arising in applied economic analysis , 1995 .

[153]  Tao Wang,et al.  A Positive Algorithm for the Nonlinear Complementarity Problem , 1995, SIAM J. Optim..

[154]  G. Stavroulakis Optimal prestress of structures with frictional unilateral contact interfaces , 1995 .

[155]  M. Ferris,et al.  Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps , 1995 .

[156]  S. Dirkse,et al.  A Comparison of Algorithms for Large Scale Mixed Complementarity Problems , 1995 .

[157]  Olvi L. Mangasarian,et al.  Smoothing methods for convex inequalities and linear complementarity problems , 1995, Math. Program..

[158]  J. Trinkle,et al.  On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction , 1995 .

[159]  Mounir Haddou,et al.  An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities , 1995, Math. Program..

[160]  G. Stavroulakis Optimal prestress of cracked unilateral structures: finite element analysis of an optimal control problem for variational inequalities , 1995 .

[161]  S. Dirkse,et al.  Mcplib: a collection of nonlinear mixed complementarity problems , 1995 .

[162]  S. Dirkse,et al.  Solver: A Non-Monotone Stabilization Scheme for Mixed Complementarity Problems , 1995 .

[163]  S. Dirkse,et al.  The path solver: a nommonotone stabilization scheme for mixed complementarity problems , 1995 .

[164]  Michal Kočvara,et al.  On the Solution of Optimum Design Problems with Variational Inequalities , 1995 .

[165]  A. Klarbring,et al.  Truss topology optimization including unilateral contact , 1995 .

[166]  Patrick T. Harker,et al.  A continuation method for monotone variational inequalities , 1995, Math. Program..

[167]  J. J. Moré,et al.  Smoothing of mixed complementarity problems , 1995 .

[168]  T. Rutherford,et al.  Regular Flexibility of Nested CES Functions , 1995 .

[169]  A. Klarbring Large displacement frictional contact: a continuum framework for finite element discretization , 1995 .

[170]  A. Klarbring,et al.  Sequential quadratic programming for non-linear elastic contact problems , 1995 .

[171]  Zhi-Quan Luo,et al.  Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints , 1996, Math. Program..

[172]  P. Tseng,et al.  Modified Projection-Type Methods for Monotone Variational Inequalities , 1996 .

[173]  F. Tin-Loi,et al.  Nonlinear analysis of semirigid frames: A parametric complementarity approach , 1996 .

[174]  Michael C. Ferris,et al.  Convergence of an Infeasible Interior-Point Algorithm from Arbitrary Positive Starting Points , 1996, SIAM J. Optim..

[175]  Jeffrey C. Trinkle,et al.  Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction , 1996, Math. Program..

[176]  Michael C. Ferris,et al.  A pathsearch damped Newton method for computing general equilibria , 1996, Ann. Oper. Res..

[177]  Masao Fukushima,et al.  Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach , 1996, SIAM J. Optim..

[178]  Tao Wang,et al.  An interior point potential reduction method for constrained equations , 1996, Math. Program..

[179]  Nicholas I. M. Gould,et al.  Numerical experiments with the LANCELOT package (release A) for large-scale nonlinear optimization , 1996, Math. Program..

[180]  F. Tin-Loi,et al.  LARGE DISPLACEMENT ELASTOPLASTIC ANALYSIS OF SEMIRIGID STEEL FRAMES , 1996 .

[181]  Jeffrey C. Trinkle,et al.  A complementarity approach to a quasistatic multi-rigid-body contact problem , 1996, Comput. Optim. Appl..

[182]  Olvi L. Mangasarian,et al.  A class of smoothing functions for nonlinear and mixed complementarity problems , 1996, Comput. Optim. Appl..

[183]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[184]  Stephen J. Wright,et al.  A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems , 1996, Math. Oper. Res..

[185]  M. Florian,et al.  O-D Demand Adjustment Problem with Congestion: Part I. Model Analysis and Optimality Conditions , 1996 .

[186]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[187]  Jorge J. Moré,et al.  Global Methods for Nonlinear Complementarity Problems , 1994, Math. Oper. Res..

[188]  Michael C. Ferris,et al.  QPCOMP: A quadratic programming based solver for mixed complementarity problems , 1997, Math. Program..

[189]  H. Kuk On equilibrium points in bimatrix games , 1996 .

[190]  Michael C. Ferris,et al.  A Comparison of Large Scale Mixed Complementarity Problem Solvers , 1997, Comput. Optim. Appl..

[191]  Michael C. Ferris,et al.  Complementarity and variational problems : state of the art , 1997 .

[192]  M. Anitescu,et al.  Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems , 1997 .

[193]  Jeffrey C. Trinkle,et al.  Dynamic multi-rigid-body systems with concurrent distributed contacts , 1997, Proceedings of International Conference on Robotics and Automation.

[194]  ANDERS KLARBRING,et al.  Existence of Solutions to Discrete Semicoercive Frictional Contact Problems , 1998, SIAM J. Optim..

[195]  G. Stavroulakis Multibody Dynamics with Unilateral Contacts by Friedrich Pfeiffer and Christoph Glocker, Wiley, New York, 1996 , 1998 .

[196]  Michal Kočvara,et al.  Nonsmooth approach to optimization problems with equilibrium constraints : theory, applications, and numerical results , 1998 .

[197]  Michael C. Ferris,et al.  Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control , 1998, INFORMS J. Comput..

[198]  Thomas F. Rutherford,et al.  Applied General Equilibrium Modeling with MPSGE as a GAMS Subsystem: An Overview of the Modeling Framework and Syntax , 1999 .

[199]  A. Klarbring,et al.  Optimization of Structures in Unilateral Contact , 1999 .