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Minimax problems of discrete optimization invariant under majority operators

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2014年第8期54卷 1327-1336页

作者： Vodolazskii, E. V. Flach, B. Schlesinger, M. I. Int Sci Educ Ctr UA-03680 Kiev Ukraine Czech Tech Univ Prague 16636 Czech Republic

A special class of discrete optimization problems that are stated as a minimax modification of the constraint satisfaction problem is studied. The minimax formulation of the problem generalizes the classical problem to realistic situations where the constraints order the elements of the set by the degree of their feasibility, rather than defining a dichotomy between feasible and infeasible subsets. The invariance of this ordering under an operator is defined, and the discrete minimization of functions invariant under majority operators is proved to have polynomial complexity. A particular algorithm for this minimization is described.

关键词： discrete optimization problem minimax modification solution algorithm

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Generalized Nash Equilibrium Problems

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ANNALS OF OPERATIONS RESEARCH 2010年第1期175卷 177-211页

作者： Facchinei, Francisco Kanzow, Christian Univ Roma La Sapienza Dept Comp & Syst Sci A Ruberti Via Ariosto 25 I-00185 Rome Italy Univ Wurzburg Inst Math D-97074 Wurzburg Germany

The Generalized Nash Equilibrium Problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main prop... 详细信息

关键词： Nash Equilibrium Problem Pseudo game Social equilibrium Coupled constraints Existence Stability solution algorithm

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MARKOV RELIABILITY MODELS FOR DIGITAL FLIGHT CONTROL-SYSTEMS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1989年第2期12卷 209-219页

作者： MCGOUGH, J REIBMAN, A TRIVEDI, K DUKE UNIV DEPT COMP SCIDURHAMNC 27706

The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The authors begin their discussion of flight control system reliability models with definitions of key terms. They then construct a single-fault one-processor model based on the results of fault-injection experiments. To illustrate more complex system models, they consider several models of a triple modular redundant system. Once they have constructed some representative Markov reliability models, they discuss numerical techniques for their solution. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution.

关键词： Digital Flight Control System Fault Injection Cumulative Distribution Function Numerical Integration Comparators Electromagnetic Interference Flight Control Computer Gaussian Elimination solution algorithm Operating Systems

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Guaranteed Approach for Orbit Determination with Limited Error Measurements

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2013年第4期36卷 1186-1193页

作者： Khutorovsky, Zakhary N. Samotokhin, Alexander S. Alfriend, Kyle T. Interstate Joint Stock Corp Vympel Tech Sci Moscow 125319 Russia Interstate Joint Stock Corp Vympel Sect Ballist & Nav Moscow 125319 Russia MV Keldysh Appl Math Inst Moscow 125047 Russia Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA

A nonstatistical statement of the orbit determination of a near-Earth space object in Earth orbit with certain limitations on the measurement errors is considered. The optimization criterion and the algorithms satisfying the limited error criterion are given. As distinguished from the traditionally used least-squares method, the interpolated algorithms are adapted to the measurement errors and always provide a guaranteed error range of the estimated parameters. The central algorithms, optimal in measurement errors in the minimax statement, have robust properties with regard to such errors. The projective robust-interpolated algorithms are independent of the measurement error upper limit. Computational schemes are given for the most practically interesting central and projective algorithms. The accuracy characteristics of such algorithms are given for different distributions of measurement errors using a mathematical simulation for typical situations occurring in the maintenance of a space objects catalog. It is demonstrated that the errors in the orbit determination of a space object using this nonstatistical approach may be less than the least-squares method errors.

关键词： Orbit Determination Earth Radar Measurement Linear Programming Space Surveillance solution algorithm Power Engineering Earth Gravitation Nonlinear Systems Solar Radiation

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Quaternion Analysis Tools for Engineering and Scientific Applications

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第2期32卷 686-693页

作者： Turner, James D. Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA

QUATERNION algebra has found a number of applications for engineering and scientific problems, including fluid mechanics [1], quantum mechanics [2,3], robotics [4,5], and spacecraft attitude control [5,6]. Unfortunate... 详细信息

关键词： Gaussian Elimination FORTRAN Computing Newton's Method Spacecraft Attitude Lyapunov Equation Search algorithm Numerical algorithms solution algorithm Fluid Mechanics

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STABILIZATION OF COMPUTATIONAL PROCEDURES FOR CONSTRAINED DYNAMICAL-SYSTEMS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1988年第4期11卷 365-370页

作者： PARK, KC CHIOU, JC UNIV COLORADO CTR SPACE STRUCT & CONTROLS BOULDER CO 80309 USA

A new stabilization method of treating constraints in multibody dynamical systems is presented. By tailoring a penalty form of the constraint equations, the method achieves stabilization without artificial damping and yields a companion matrix differential equation for the constraint forces; hence, the constraint forces are obtained by integrating the companion differential equation for the constraint forces in time. A principal feature of the method is that the errors committed in each constraint condition decay with its corresponding characteristic time scale associated with its constraint force. Numerical experiments indicate that the method yields a marked improvement over existing techniques. (Author)

关键词： Holonomic Constraints solution algorithm Fluid Structure Interaction Robotic Manipulators Computing Large Space Structures Coriolis Force Satellites

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Three-dimensional flow computation around a projectile overtaking a preceding shock wave

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JOURNAL OF SPACECRAFT AND ROCKETS 1998年第5期35卷 619-625页

作者： Watanabe, R Fujii, K Higashino, F Tokyo Noko Univ Dept Mech Syst Engn Tokyo Japan Inst Space & Astronaut Sci Kanagawa 229 Japan

A numerical simulation of the flowfield around a projectile overtaking a preceding shock wave is carried out by solving the three-dimensional, thin layer Navier-Stokes equations. A domain decomposition method with the fortified solution algorithm interface scheme is used to supply reasonable grid configurations for such an unsteady flowfield. Computed results show that complicated interaction flowfields are observed while overtaking the shock wave. The results of the two- and three-dimensional flowfield computations are compared, and the characteristic features of the three-dimensional flowfield are shown. Time histories of the aerodynamic forces show that the projectile suffers strong asymmetric forces while overtaking the shock wave, which may make the trajectory of the projectile unstable.

关键词： Conical Shock Wave Projectiles Aerodynamic Force Wake Vortices Navier Stokes Equations Adverse Pressure Gradient Boundary Layer Separation Domain Decomposition Methods solution algorithm Supersonic Speed

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A NEW REINFORCING STEEL MODEL WITH BOND-SLIP

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STRUCTURAL ENGINEERING AND MECHANICS 1995年第4期3卷 299-312页

作者： KWAK, HG FILIPPOU, FC UNIV CALIF BERKELEY DEPT CIVIL ENGNBERKELEYCA 94720

A new reinforcing steel model which is embedded inside a concrete element and also accounts for the effect of bond-slip is developed. Unlike the classical bond-link or bond-zone element using double nodes, the proposed model is considering the bond-slip effect without taking double nodes by incorporation of the equivalent steel stiffness. After calculation of nodal displacements, the deformation of steel at each node can be found through the back-substitution technique from the first to the final steel element using a governing equation constructed based on the equilibrium at each node of steel and the compatibility condition between steel and concrete. This model results in significant savings in the number of nodes needed to account for the effect of bond-slip, in particular, when the-model is used for three dimensional finite element problems. Moreover a new nonlinear solution scheme is developed in connection with this model. Finally, correlation studies between analytical and experimental results and several parameter studies are conducted with the objective to establish the validity of the proposed model.

关键词： BOND-SLIP STEEL MODEL DOUBLE NODE solution algorithm EQUILIBRIUM

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EXTENSION OF THE LAMBDA-FORMULATION TO IMPERFECT GAS-FLOWS

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AIAA JOURNAL 1992年第11期30卷 2785-2788页

作者： LENTINI, D Universita degli Studi di Roma "La Sapienza " 1-00184 Rome Italy

The λ formulation has proven to be a powerful tool for the numerical solution of compressible flows of a perfect gas. In this note we extend the λ formulation to (inert) flows of thermally perfect gas with cp varying as a function of the temperature T. Such gases are sometimes referred to as 'imperfect gases'. The resulting formulation is extremely simple and involves a minimum computational overhead in comparison to the perfect gas case. Indeed, existing algorithms for a perfect gas can easily be upgraded with a minimum coding effort, without fundamentally altering their structure. The proposed formulation is applied to the computation of flow in a quasi-one-dimensional nozzle to prove the workability of this approach and to demonstrate the differences with respect to a perfect gas computation. It is apparent, however, that the range of application of the present formulation is completely general.

关键词： Perfect Gas One Dimensional Flow Chemical Equilibrium Shock Tunnels Stagnation Temperature Chemically Reacting Flow Continuity Equation Stagnation Enthalpy Vibrational Energy solution algorithm

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ROLE OF ARTIFICIAL VISCOSITY IN EULER AND NAVIER-STOKES SOLVERS

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AIAA JOURNAL 1991年第4期29卷 555-559页

作者： MAHAJAN, AJ DOWELL, EH BLISS, DB NASA LEWIS RES CTRCLEVELANDOH 44135 DUKE UNIV DEPT MECH ENGN & MAT SCIDURHAMNC 27706 DUKE UNIV SCH ENGNDURHAMNC 27706

A method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the Navier-Stokes equations. The stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity. The eigenvalues were determined for a small time-dependent perturbation about a steady inviscid flow over a NACA 0012 airfoil at a Mach number of 0.8 and angle of attack of 0 deg. The method has been applied to inviscid flows here, but as discussed is also applicable to viscous flows. The movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied. The stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time-marching scheme are also presented. The eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity, but also for the effects of different forms of artificial viscosity.

关键词： Eddy Viscosity Navier Stokes Solver Flow Conditions Navier Stokes Equations Constellations Drag Coefficient NACA 0012 Angle of Attack solution algorithm Baldwin Lomax Turbulence Model

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