System Modelling and Optimization

In (Boggs, Tolle and Kearsley, 1994) the authors introduced an effective algorithm for general large scale nonlinear programming problems. In this paper we describe the theoretical foundation for this method. The algorithm is based on a trust region, sequential quadratic programming (SQP) technique and uses a special auxiliary function, called a merit function or line-search function, for assessing the steps that are generated. A global convergence theorem for a basic version of the algorithm is stated and its proof is outlined.

[1]  S. S. Sengupta,et al.  The traveling salesman problem , 1961 .

[2]  A. Perelson,et al.  Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection , 1995, Nature.

[3]  Harilaos N. Psaraftis,et al.  A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem , 1980 .

[4]  Application of generalized raiffa solution to multicriteria bargaining support , 1988 .

[5]  Kaddour Najim,et al.  Adaptive Linear Quadratic Control of an Extractor , 1988 .

[6]  K. Kiwiel.  The Efficiency of Subgradient Projection Methods for Convex Optimization , 1996 .

[7]  Walter Ukovich,et al.  Minimization of logistic costs with given frequencies , 1997 .

[8]  Rainer Schrader,et al.  A setup heuristic for interval orders , 1985 .

[9]  L. Kruś,et al.  Solution concepts in multicriteria cooperative games without side payments , 1996 .

[10]  G. Chow.  Analysis and control of dynamic economic systems , 1975 .

[11]  J. Dolezal,et al.  Mathematical modelling of HIV infection therapy. , 1995, International journal of immunopharmacology.

[12]  K. Najim.  Multivariable control of a liquid-liquid extraction column using a probabilistic automaton , 1988 .

[13]  K. Kiwiel.  Finding normal solutions in piecewise linear programming , 1995 .

[14]  L. Kruś,et al.  MCBARG - Enhanced. A System Supporting Multicriteria Bargaining , 1990 .

[15]  R. L. V. Gonzalez,et al.  Sur l'ordre de convergence des solutions discrétisées en temps et en espace de l'équation de Hamilton-Jacobi , 1992 .

[16]  P. Neittaanmäki,et al.  Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control , 1992 .

[17]  Stefan Chanas,et al.  Maximum flow in a network with fuzzy arc capacities , 1982 .

[18]  E. Schmidt,et al.  Boundary control for the heat equation with non-linear boundary condition , 1989 .

[19]  W. Hager.  Multiplier methods for nonlinear optimal control , 1990 .

[20]  Allen J. Wood,et al.  Power Generation, Operation, and Control , 1984 .

[21]  Marek Makowski,et al.  Multiple criteria analysis for water quality management in the Nitra Basin , 1996 .

[22]  S. Zenios,et al.  Constructing Optimal Samples from a Binomial Lattice , 1993 .

[23]  T. Raivio,et al.  A method to generate trajectories for minimum time climb , 1994 .

[24]  David A. Landgrebe,et al.  A survey of decision tree classifier methodology , 1991, IEEE Trans. Syst. Man Cybern..

[25]  K.K. Aggarwal,et al.  Redundancy Optimization in General Systems , 1976, IEEE Transactions on Reliability.

[26]  Kazimierz Malanowski,et al.  The Lagrange-Newton method for nonlinear optimal control problems , 1993, Comput. Optim. Appl..

[27]  Marek Makowski,et al.  Methodology and a Modular Tool for Multiple Criteria Analysis of LP Models , 1994 .

[28]  Kok Lay Teo,et al.  A Unified Computational Approach to Optimal Control Problems , 1991 .

[29]  Randolph W. Hall,et al.  Distribution Strategies that Minimize Transportation and Inventory Costs , 1985, Oper. Res..

[30]  Robert M. May,et al.  Stability and Complexity in Model Ecosystems , 2019, IEEE Transactions on Systems, Man, and Cybernetics.

[31]  Loren Platzman,et al.  Routing and scheduling , 1984, The 23rd IEEE Conference on Decision and Control.

[32]  Lucio Bianco,et al.  Exact and Heuristic Algorithms for the Jump Number Problem , 1995 .

[33]  N. Olhoff,et al.  Multiple eigenvalues in structural optimization problems , 1994 .

[34]  Marc Teboulle,et al.  Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions , 1993, SIAM J. Optim..

[35]  R. Möhring.  Algorithmic Aspects of Comparability Graphs and Interval Graphs , 1985 .

[36]  Thomas E. Hendrick,et al.  Determining Performance Appraisal Criteria For Buyers , 1988 .

[37]  M W Hirsch,et al.  Computing with dynamic attractors in neural networks. , 1995, Bio Systems.

[38]  Stephan Beckert.  Modenselektion beim Laser zur Realisierung des Synergetischen Computers , 1994 .

[39]  Paul E. Sweeney,et al.  Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography , 1992 .

[40]  P. Ciarlet,et al.  Mathematical elasticity, volume I: Three-dimensional elasticity , 1989 .

[41]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[42]  A. J. Calise,et al.  Necessary conditions for optimal pulse control , 1985 .

[43]  M. H. Breitnery,et al.  Three-dimensional Air Combat: Numerical Solution of Complex Diierential Games , 1996 .

[44]  G. Scheithauer,et al.  Modeling of packing problems , 1993 .

[45]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[46]  Stephen M. Robinson,et al.  An Implicit-Function Theorem for a Class of Nonsmooth Functions , 1991, Math. Oper. Res..

[47]  E. Maas,et al.  CROP SALT TOLERANCE–CURRENT ASSESSMENT , 1977 .

[48]  Elijah Polak,et al.  On the Use of Consistent Approximations for the Optimal Design of Beams , 1996 .

[49]  Jonathan Eckstein,et al.  Stochastic dedication: designing fixed income portfolios using massively parallel Benders decomposition , 1993 .

[50]  A. Palucka,et al.  Strength of binding between leukemic blasts and cytotoxic lymphocytes. , 1996, Cytometry.

[51]  C. Tsouris,et al.  Control of dispersed-phase volume fraction in multistage extraction columns , 1991 .

[52]  D. Elston,et al.  Calibration and validation of a modified steady-state model of crop response to saline water irrigation under conditions of transient root zone salinity , 1991 .

[53]  William Thomson,et al.  Two characterizations of the Raiffa solution , 1980 .

[54]  Bezalel Peleg.  SOLUTIONS TO COOPERATIVE GAMES WITHOUT SIDE PAYMENTS , 1963 .

[55]  Jerzy Kyparisis.  Solution differentiability for variational inequalities , 1990, Math. Program..

[56]  Antonio Albano,et al.  A Solution of the Rectangular Cutting-Stock Problem , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[57]  Andrzej P. Wierzbicki,et al.  Models and sensitivity of control systems , 1984 .

[58]  Hans-Jürgen Sebastian,et al.  Optimization-Based Computer-Aided Modelling and Design , 1992 .

[59]  Ryuichi Hirabayashi,et al.  NODE DUPLICATION LOWER BOUNDS FOR THE CAPACITATED ARC ROUTING PROBLEM , 1992 .

[60]  Yurii Nesterov,et al.  New variants of bundle methods , 1995, Math. Program..

[61]  C. E. Chidume,et al.  Approximation Methods for Nonlinear Operator-Equations of the m-Accretive Type , 1995 .

[62]  Hirotaka Nakayama,et al.  Aspiration Level Approach to Interactive Multi-Objective Programming and Its Applications , 1995 .

[63]  Jochem Zowe,et al.  A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results , 1992, SIAM J. Optim..

[64]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[65]  James W. Daniel.  The Ritz–Galerkin Method for Abstract Optimal Control Problems , 1973 .

[66]  A. Di Febbraro,et al.  Performance optimization in manufacturing systems by use of max-plus algebraic techniques , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[67]  J. Piekarski,et al.  Design Sensitivity for a Hyperelastic Rod in Large Displacement with Respect to Its Midcurve Shape , 1998 .

[68]  Lorraine R. Gardiner,et al.  Unified interactive multiple objective programming , 1994 .

[69]  K. Tanabe.  A geometric method in nonlinear programming , 1980 .

[70]  D. L. Carter,et al.  Saline and Sodic Soils , 1982, Advanced Series in Agricultural Sciences.

[71]  John R. Beaumont,et al.  Large-Scale Systems: Modeling and Control , 1983 .

[72]  Heinz H. Bauschke,et al.  On Projection Algorithms for Solving Convex Feasibility Problems , 1996, SIAM Rev..

[73]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[74]  M. BelenguerJ.,et al.  The Capacitated Arc Routing Problem , 1998 .

[75]  H. Raiffa,et al.  Decisions with Multiple Objectives , 1993 .

[76]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[77]  J. Granat,et al.  Interactive Specification of DSS User Preferences in Terms of Fuzzy Sets , 1994 .

[78]  Awi Federgruen,et al.  One warehouse multiple retailer systems with vehicle routing costs , 1990 .

[79]  K. Najim,et al.  Learning control of a pulsed liquid-liquid extraction column , 1987 .

[80]  Chengbin Chu,et al.  Supply management in assembly systems : the basic problem , 1992 .

[81]  Eckhart Blaß,et al.  Dynamic behaviour and simulation of a liquid‐liquid extraction column , 1991 .

[82]  Gerhard Gierz,et al.  Minimizing Setups for Ordered Sets: A Linear Algebraic Approach , 1983 .

[83]  K. Kiwiel.  A Dual Method for Certain Positive Semidefinite Quadratic Programming Problems , 1989 .

[84]  K. Najim,et al.  Adaptive Control of a Liquid-Liquid Extractor , 1985 .

[85]  K. Najim,et al.  Regularized pole-placement adaptive control of a liquid-liquid extraction column , 1990 .

[86]  Robert J. Vanderbei,et al.  Symmetric indefinite systems for interior point methods , 1993, Math. Program..

[87]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[88]  D. Stephany,et al.  The measurement of specific cell: cell interactions by dual-parameter flow cytometry. , 1984, Cytometry.

[89]  Vlasta Kanková.  Optimization problem with parameter and its application to the problems of two-stage stochastic nonlinear programming , 1980, Kybernetika.

[90]  J. Randall Brown,et al.  The Sharing Problem , 1979, Oper. Res..

[91]  Nicholas I. M. Gould,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[92]  M. Savelsbergh.  An efficient implementation of local search algorithms for constrained routing problems , 1990 .

[93]  Włodzimierz Ogryczak,et al.  Aspiration/Reservation-Based Decision Support—a Step Beyond Goal Programming , 1992 .

[94]  Claude Lemaréchal,et al.  An approach to variable metric bundle methods , 1993, System Modelling and Optimization.

[95]  K. Najim,et al.  Extended horizon self-tuning control of a pulsed liquid-liquid extraction column , 1989 .

[96]  R. V. Helgason,et al.  Algorithms for network programming , 1980 .

[97]  Paul Waltman,et al.  The Theory of the Chemostat , 1995 .

[98]  J. Granat,et al.  IAC-DIDAS-N A Dynamic Interactive Decision Analysis and Support System for Multicriteria Analysis of Nonlinear Models , 1988 .

[99]  Stavros A. Zenios,et al.  Stochastic-Programming Models for Portfolio Optimization with Mortgage-Backed Securities - Comprehen , 1993 .

[100]  Richard W. Eglese,et al.  Efficient Routeing for Winter Gritting , 1992 .

[101]  Ian H. Sloan,et al.  Piecewise Continuous Collocation for Integral Equations , 1983 .

[102]  Eugene M. Cliff,et al.  Range optimal trajectories for an aircraft flying in the vertical plane , 1994 .

[104]  Rein Luus,et al.  Optimization of System Reliability by a New Nonlinear Integer Programming Procedure , 1975, IEEE Transactions on Reliability.

[105]  E B Lee,et al.  Foundations of optimal control theory , 1967 .

[106]  H. Tuy.  Global Minimization of a Difference of Two Convex Functions , 1987 .

[107]  Friedrich Stummel,et al.  Diskrete Konvergenz linearer Operatoren. II , 1971 .

[108]  Shi Dinghua,et al.  A New Heuristic Algorithm for Constrained Redundancy-Optimization in Complex Systems , 1987, IEEE Transactions on Reliability.

[109]  M A Nowak,et al.  Antigenic diversity thresholds and the development of AIDS. , 1991, Science.

[110]  Panos M. Pardalos,et al.  Quadratic programming with one negative eigenvalue is NP-hard , 1991, J. Glob. Optim..

[111]  A. Renaud,et al.  Daily generation scheduling optimization with transmission constraints: a new class of algorithms , 1992 .

[112]  Yuri G. Evtushenko,et al.  Stable barrier-projection and barrier-Newton methods in linear programming , 1994, Comput. Optim. Appl..

[113]  Xiaolan Xie,et al.  Supply management in assembly systems , 1993 .

[114]  A. Perelson,et al.  Dynamics of HIV infection of CD4+ T cells. , 1993, Mathematical biosciences.

[115]  J. Banks,et al.  Discrete-Event System Simulation , 1995 .

[116]  C. Hwang,et al.  Optimization Techniques for System Reliability with RedundancyߞA Review , 1977, IEEE Transactions on Reliability.

[117]  Sharat Israni,et al.  Two-dimensional cutting stock problem research: A review and a new rectangular layout algorithm , 1982 .

[118]  R. Bellman,et al.  Dynamic Programming and the Reliability of Multicomponent Devices , 1958 .

[119]  Angela Di Febbraro,et al.  INTRANET: A new simulation tool for intermodal transportation systems , 1996, Simul. Pract. Theory.

[120]  Alan J. King,et al.  Stochastic Programming Problems: Examples from the Literature , 1988 .

[121]  Zhenyu Li,et al.  A compaction algorithm for non-convex polygons and its application , 1993, SCG '93.

[122]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[123]  G. David Forney,et al.  Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference , 1972, IEEE Trans. Inf. Theory.

[124]  K. Malanowski.  Two norm approach in stability analysis of optimization and optimal control problems , 1996 .

[125]  Nicos Christofides,et al.  An Algorithm for Two-Dimensional Cutting Problems , 1977, Oper. Res..

[126]  E. Kalai,et al.  OTHER SOLUTIONS TO NASH'S BARGAINING PROBLEM , 1975 .

[127]  Shiv K. Gupta,et al.  The Systems Approach in an Information Society: A Reconsideration , 1985 .

[128]  Roy L. Streit,et al.  Frequency line tracking using hidden Markov models , 1990, IEEE Trans. Acoust. Speech Signal Process..

[129]  J. Bluestone,et al.  Quantitative measurements of the specificity and kinetics of conjugate formation between cloned cytotoxic T lymphocytes and splenic target cells by dual parameter flow cytometry. , 1985, Journal of Immunology.

[130]  E. Barron,et al.  The Bellman equation for minimizing the maximum cost , 1989 .

[131]  J. Reddy.  Energy and variational methods in applied mechanics : with an introduction to the finite element method , 1984 .

[132]  R. Zinkernagel,et al.  T-cell-mediated immunopathology versus direct cytolysis by virus: implications for HIV and AIDS. , 1994, Immunology today.

[133]  Van Nostrand,et al.  Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm , 1967 .

[134]  Gintautas Dzemyda,et al.  Multiple criteria decision support system: methods, user's interface and applications , 1994 .

[135]  B. N. Pshenichnyi,et al.  Numerical Methods in Extremal Problems. , 1978 .

[136]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[137]  Mark D. Treleven,et al.  A risk/benefit analysis of sourcing strategies: Single vs. multiple sourcing , 1988 .

[138]  Edward Szczerbicki,et al.  Model-based generation of knowledge for autonomous systems , 1994 .

[139]  R. Rockafellar,et al.  The Optimal Recourse Problem in Discrete Time: $L^1 $-Multipliers for Inequality Constraints , 1978 .

[140]  A. Miele,et al.  A transformation technique for optimal control problems with partially linear state inequality constraints , 1979 .

[141]  A. Dinar,et al.  Simulated crop water production functions for several crops when irrigated with saline waters , 1986 .

[142]  Stefan Chanas,et al.  Integer flows in network with fuzzy capacity constraints , 1986, Networks.

[143]  H. O. Fattorini,et al.  Optimal Problems for Nonlinear Parabolic Boundary Control Systems , 1994 .

[144]  R. Lewis,et al.  A State-of-the-Art Discussion on the Solvent Extraction Reagents Used for the Recovery of Copper from Dilute Sulfuric Acid Leach Solutions , 1987 .

[145]  Y. Censor,et al.  Proximal Minimization Algorithm with D-Functions 1'2 , 1992 .

[146]  Michael Florian,et al.  Network Equilibrium Models with Combined Modes , 1994, Transp. Sci..

[147]  K. Kiwiel.  Block-iterative surrogate projection methods for convex feasibility problems , 1995 .

[148]  R. Aumann.  The core of a cooperative game without side payments , 1961 .

[149]  Endre Boros,et al.  Closed Form Two-Sided Bounds for Probabilities that At Least r and Exactly r Out of n Events Occur , 1989, Math. Oper. Res..

[150]  John E. Rijnsdorp,et al.  Advanced process control: W. Harmon Ray , 1982, Autom..

[151]  M. A. Hughes,et al.  The modelling of equilibrium data for the liquid-liquid extraction of metals , 1975 .

[152]  C. Bert,et al.  Introduction to Optimization of Structures , 1990 .

[153]  K. Kiwiel.  A Cholesky dual method for proximal piecewise linear programming , 1994 .

[154]  C. R. Cutler,et al.  Optimal Solution of Dynamic Matrix Control with Linear Programing Techniques (LDMC) , 1985, 1985 American Control Conference.

[155]  Elijah Polak,et al.  On the use of consistent approximations in the solution of semi-infinite optimization and optimal control problems , 1993, Math. Program..

[156]  Tarik Al-Ani,et al.  Parameters identification of a time-varying stochastic dynamic systems using Viterbi algorithm , 1996 .

[157]  K. Kiwiel.  A Method for Solving Certain Quadratic Programming Problems Arising in Nonsmooth Optimization , 1986 .

[158]  L. Adleman,et al.  T-cell homeostasis: implications in HIV infection . , 1993, Journal of acquired immune deficiency syndromes.

[159]  H. Haken.  Synergetics: an Introduction, Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology , 1977 .

[160]  B. Widrow,et al.  Neural networks for self-learning control systems , 1990, IEEE Control Systems Magazine.

[161]  K. Kiwiel.  The efficiency of subgradient projection methods for convex optimization, part I: general level methods , 1996 .

[162]  Joseph Shalhevet,et al.  Using water of marginal quality for crop production: major issues , 1994 .

[163]  Yacov Y. Haimes,et al.  Approach to performance and sensitivity multiobjective optimization: The goal attainment method , 1975 .

[164]  C. Goh,et al.  Direct training method for a continuous-time nonlinear optimal feedback controller , 1995 .

[165]  V. Komkov.  Optimal shape design for elliptic systems , 1986 .

[166]  Krzysztof C. Kiwiel,et al.  Surrogate Projection Methods for Finding Fixed Points of Firmly Nonexpansive Mappings , 1997, SIAM J. Optim..

[167]  J. Jacquez,et al.  AIDS: the epidemiological significance of two different mean rates of partner change. , 1990, IMA journal of mathematics applied in medicine and biology.

[168]  W. Clark,et al.  Interpretation of 51Cr-release data: a kinetic analysis. , 1978, Journal of immunology.

[169]  R. González,et al.  A numerical procedure for minimizing the maximum cost , 1996 .

[170]  Fumiko Seo,et al.  Multiple Criteria Decision Analysis in Regional Planning: Concepts, Methods and Applications , 1987 .

[171]  J. Fowler.  The linear-quadratic formula and progress in fractionated radiotherapy. , 1989, The British journal of radiology.

[172]  Michel Gendreau,et al.  Arc Routing Problems, Part II: The Rural Postman Problem , 1995, Oper. Res..

[173]  D. Seborg,et al.  A linear programming approach for multivariable feedback control with inequality constraints , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[174]  Jitka Dupacová,et al.  Multistage stochastic programs: The state-of-the-art and selected bibliography , 1995, Kybernetika.

[175]  Wen Lea Pearn,et al.  Approximate solutions for the capacitated arc routing problem , 1989, Comput. Oper. Res..

[176]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[177]  Lech Krus,et al.  Onn-person noncooperative multicriteria games described in strategic form , 1994, Ann. Oper. Res..

[178]  A. Palucka,et al.  Kinetic analysis of cytotoxic lymphocyte-target cell interaction as quantified by dual parameter flow cytometry. , 1993, Cytometry.

[179]  Kaisa Miettinen,et al.  An interactive method for nonsmooth multiobjective optimization with an application to optimal control , 1993 .

[180]  B. Rousselet,et al.  A Finite Strain Rod Model and Its Design Sensitivity , 1992 .

[181]  C. Leake.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[182]  J. Castro,et al.  An implementation of linear and nonlinear multicommodity network flows , 1996 .

[183]  P. Yu,et al.  Domination structures and multicriteria problems in n-person games , 1977 .

[184]  W Düchting,et al.  Radiogenic responses of normal tissue induced by fractionated irradiation--a simulation study. I. Acute effects. , 1995, Strahlentherapie und Onkologie : Organ der Deutschen Rontgengesellschaft ... [et al].

[185]  Philip E. Gill,et al.  Practical optimization , 1981 .

[186]  G. Dzemyda,et al.  Control of the HIV/AIDS Infection Spread , 1993 .

[187]  K. Malanowski.  Second-order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces , 1992 .

[188]  E. Polak.  On the mathematical foundations of nondifferentiable optimization in engineering design , 1987 .

[189]  T Hraba,et al.  Model-based analysis of CD4+ lymphocyte dynamics in HIV infected individuals. , 1990, Immunobiology.

[190]  Ranga V. Ramasesh,et al.  Sole Versus Dual Sourcing in Stochastic Lead-Time s, Q Inventory Models , 1991 .

[191]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[192]  H. Raiffa.  21. Arbitration Schemes for Generalized Two-person Games , 1953 .

[193]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[194]  Richard Edwin Stearns.  On the axioms for a cooperative game without side payments , 1964 .

[195]  Wlodzimierz Ogryczak,et al.  Modular Optimizer for Mixed Integer Programming MOMIP Version 2.1 , 1993 .

[196]  Per Olov Lindberg,et al.  A descent proximal level bundle method for convex nondifferentiable optimization , 1995, Oper. Res. Lett..

[197]  R.B. Misra,et al.  Peculiarities in Optimal Redundancy for a Bridge Network , 1979, IEEE Transactions on Reliability.

[198]  Robin J. Evans,et al.  Multiple target tracking and multiple frequency line tracking using hidden Markov models , 1991, IEEE Trans. Signal Process..

[199]  H. Maurer,et al.  Sensitivity analysis for parametric control problems with control-state constraints , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[200]  M. Eigen,et al.  The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. , 1977, Die Naturwissenschaften.

[201]  W Düchting,et al.  Radiogenic responses of normal cells induced by fractionated irradiation--a simulation study. Part II. Late responses. , 1995, Strahlentherapie und Onkologie : Organ der Deutschen Rontgengesellschaft ... [et al].

[202]  JoséFernando Oliveira,et al.  An improved version of Wang's algorithm for two-dimensional cutting problems , 1990 .

[203]  Cheng Hsu,et al.  Information modeling for computerized manufacturing , 1990, IEEE Trans. Syst. Man Cybern..

[204]  Costas Tsouris,et al.  Application of the ultrasonic technique for real-time holdup monitoring for the control of extraction columns , 1990 .

[205]  Marek Makowski.  LP-DIT Data Interchange Tool for Linear Programming Problems (version 1.20) , 1994 .

[206]  Charles S. Kenney,et al.  Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity , 1981 .

[207]  R. González,et al.  On deterministic control problems: An approximation procedure for the optimal cost , 1983, The 22nd IEEE Conference on Decision and Control.

[208]  Wen Lea Pearn,et al.  Augment-insert algorithms for the capacitated arc routing problem , 1991, Comput. Oper. Res..

[209]  John E. Beasley,et al.  An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure , 1985, Oper. Res..

[210]  Eliezer Kreindler.  Optimal control: An introduction to the theory and its applications: by Michael Athans and Peter L. Falb. 879 pages, diagrams, 6 × 9 in. New York, McGraw-Hill Book Co., 1966. Price, $19.95 , 1967 .

[211]  J. Daniel.  On the approximate minimization of functionals , 1969 .

[212]  R. Makinen.  On numerical methods for state constrained optimal shape design problems , 1989 .

[213]  Jonathan F. Bard,et al.  Short-Term Scheduling of Thermal-Electric Generators Using Lagrangian Relaxation , 1988, Oper. Res..

[214]  C. Benson,et al.  Viral Dynamics in Human Immunodeficiency Virus Type 1 Infection , 1995 .

[215]  K. Kiwiel.  Methods of Descent for Nondifferentiable Optimization , 1985 .

[216]  Harilaos N. Psaraftis,et al.  k-Interchange procedures for local search in a precedence-constrained routing problem , 1983 .

[217]  J. Zowe,et al.  Relaxed outer projections, weighted averages and convex feasibility , 1990 .

[218]  A. Wierzbicki.  A Mathematical Basis for Satisficing Decision Making , 1982 .

[219]  Walter Ukovich,et al.  Minimizing Transportation and Inventory Costs for Several Products on a Single Link , 1994, Oper. Res..

[220]  Gilbert Laporte,et al.  Arc Routing Problems, Part I: The Chinese Postman Problem , 1995, Oper. Res..

[221]  Ira M. Longini,et al.  The stages of HIV infection: waiting times and infection transmission probabilities , 1989 .

[222]  Andrzej P. Wierzbicki,et al.  Aspiration Based Decision Support Systems: Theory, Software and Applications , 1989 .