This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: - optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. - emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. - gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. - auxiliary function, generalized penalty function, modified Lagrange func tion. - convexity, quasiconvexity, abstract convexity.
Preface. Part I: Numerical methods and applications. 1. An approach to constructing generalized penalty functions; M. Andramonov. 2. An exact method for solving the subproblem of the cutting angle method of global optimization; D.A. Babayev. 3. On modeling risk in Markov decision processes; S. Levitt, A. Ben-Israel. 4. Multiplicative programming and beyond via C-programming; L. Churilov, M. Sniedovich. 5. Computing optimal control on matlab - the SCOM package and economic growth models; B.D. Craven, S.M.N. Islam. 6. Stochastic optimal control of a solar car; J. Boland, et al. 7. On optimal algorithms in emergent computation; V. Korotkich. 8. Optimal estimation of signal parameters using bilinear observations; P.M. Pardalos, et al. 9. On an extremal problem arising in queueing theory and telecommunications; M. Peake, C.E.M. Pearce. 10. Level functions of some optimal value functions; H. Xu. 11. Regularized gap functions and D-gap functions for nonsmooth variational inequalities; H. Xu. Part II: Theory of optimization and related topics. 12. Convex spectral functions of compact operators, Part II: lower semicontinuity and rearrangement invariance; J.M. Borwein, et al. 13. Some inequalities for Riemann-Stieltjes integral and applications; S.S. Dragomir. 14. Prox-regularity and subjets; A. Eberhard. 15. Concerning differentiability properties of locally Lipschitz functions; J.R.Giles, S. Sciffer. 16. Laurent series for the inversion of perturbed linear operators on Hilbert space; Ph. Howlett, K. Avrachenkov. 17. The extremal principle and its applications to optimization and economics; B.S. Mordukhovich. 18. Generic convergence of infinite products of nonexpansive mappings in Banach and hyperbolic spaces; S. Reich, A.J. Zaslavski. 19. Recession cones of star-shaped and co-star-shaped sets; A.P. Shveidel. 20. Does continuity of convex-valued maps survive under intersection? A. Vladimirov. 21. Existence and structure of solutions of optimal control problems; A.J. Zaslavski. References.
This volume contains, in part, a selection of papers presented at the sixth Australian Optimization Day Miniconference (Ballarat, 16 July 1999), and the Special Sessions on Nonlinear Dynamics and Optimization and Operations Re search - Methods and Applications, which were held in Melbourne, July 11-15 1999 as a part of the Joint Meeting of the American Mathematical Society and Australian Mathematical Society. The editors have strived to present both con tributed papers and survey style papers as a more interesting mix for readers. Some participants from the meetings mentioned above have responded to this approach by preparing survey and 'semi-survey' papers, based on presented lectures. Contributed paper, which contain new and interesting results, are also included. The fields of the presented papers are very large as demonstrated by the following selection of key words from selected papers in this volume: - optimal control, stochastic optimal control, MATLAB, economic models, implicit constraints, Bellman principle, Markov process, decision-making under uncertainty, risk aversion, dynamic programming, optimal value function. - emergent computation, complexity, traveling salesman problem, signal estimation, neural networks, time congestion, teletraffic. - gap functions, nonsmooth variational inequalities, derivative-free algo rithm, Newton's method. - auxiliary function, generalized penalty function, modified Lagrange func tion. - convexity, quasiconvexity, abstract convexity.
I Numerical Methods and Applications.- 1 An Approach to Constructing Generalized Penalty Functions.- 2 An Exact Method for Solving the Subproblem of the Cutting Angle Method of Global Optimization.- 3 On Modeling Risk in Markov Decision Processes.- 4 Multiplicative Programming and Beyond Via C-Programming.- 5 Computing Optimal Control on Matlab - The Scom Package and Economic Growth Models.- 6 Stochastic Optimal Control of a Solar Car.- 7 On Optimal Algorithms in Emergent Computation.- 8 Optimal Estimation of Signal Parameters Using Bilinear Observations.- 9 On an Extremal Problem Arising in Queueing Theory and Telecommunications.- 10 Level Functions of Some Optimal Value Functions.- 11 Regularized Gap Functions and D-Gap Functions for Nons Mooth Variational Inequalities.- II Theory of Optimization and Related Topics.- 12 Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance.- 13 Some Inequalities for Riemann-Stieltjes Integral and Applications.- 14 Prox-Regularity and Subjets.- 15 Concerning Differentiability Properties of Locally Lipschitz Functions.- 16 Laurent Series for the Inversion of Perturbed Linear Operators on Hilbert Space.- 17 The Extremal Principle and Its Applications to Optimization and Economics.- 18 Generic Convergence of Infinite Products of Nonexpansive Mappings In Banach and Hyperbolic Spaces.- 19 Recession Cones of Star-Shaped and Co-Star-Shaped Sets.- 20 Does Continuity of Convex-Valued Maps Survive Under Intersection?.- 21 Existence and Structure of Solutions of Optimal Control Problems.
Inhaltsverzeichnis
Preface. Part I: Numerical methods and applications. 1. An approach to constructing generalized penalty functions; M. Andramonov. 2. An exact method for solving the subproblem of the cutting angle method of global optimization; D.A. Babayev. 3. On modeling risk in Markov decision processes; S. Levitt, A. Ben-Israel. 4. Multiplicative programming and beyond via C-programming; L. Churilov, M. Sniedovich. 5. Computing optimal control on matlab - the SCOM package and economic growth models; B.D. Craven, S.M.N. Islam. 6. Stochastic optimal control of a solar car; J. Boland, et al. 7. On optimal algorithms in emergent computation; V. Korotkich. 8. Optimal estimation of signal parameters using bilinear observations; P.M. Pardalos, et al. 9. On an extremal problem arising in queueing theory and telecommunications; M. Peake, C.E.M. Pearce. 10. Level functions of some optimal value functions; H. Xu. 11. Regularized gap functions and D-gap functions for nonsmooth variational inequalities; H. Xu. Part II: Theory of optimization and related topics. 12. Convex spectral functions of compact operators, Part II: lower semicontinuity and rearrangement invariance; J.M. Borwein, et al. 13. Some inequalities for Riemann-Stieltjes integral and applications; S.S. Dragomir. 14. Prox-regularity and subjets; A. Eberhard. 15. Concerning differentiability properties of locally Lipschitz functions; J.R.Giles, S. Sciffer. 16. Laurent series for the inversion of perturbed linear operators on Hilbert space; Ph. Howlett, K. Avrachenkov. 17. The extremal principle and its applications to optimization and economics; B.S. Mordukhovich. 18. Generic convergence of infinite products of nonexpansive mappings in Banach and hyperbolic spaces; S. Reich, A.J. Zaslavski. 19. Recession cones of star-shaped and co-star-shaped sets; A.P. Shveidel. 20. Does continuity of convex-valued maps survive under intersection? A. Vladimirov. 21. Existence and structure of solutions of optimal control problems; A.J. Zaslavski. References.
