Ebook: Optimization and Related Topics

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.

---

The book, comprised predominantly of survey chapters, is a collection of recent results in various fields of theoretical and applied optimization and related topics. It contains survey papers on second order nonsmooth analysis, based on subjects, multiplicative programs and c-programming, optimal algorithms in emergent computation, the extremal principle and its applications, turnpike property for variational problems, asymptotic behavior of random infinite products of some operators, inequalities for Riemann-Stieltjes integral. Other topics covered include nonsmooth analysis and analysis of linear operators and set-valued mappings, numerical methods and generalized penalty functions, applied optimal control problems and Markov decision processes, optimal estimation of signal parameters and the problem of maximal time congestion.
Audience: Specialists in optimization, mathematical programming, convex analysis, nonsmoooth analysis, engineers using mathematical tools and optimization technique, specialists in mathematical modeling.

---

The book, comprised predominantly of survey chapters, is a collection of recent results in various fields of theoretical and applied optimization and related topics. It contains survey papers on second order nonsmooth analysis, based on subjects, multiplicative programs and c-programming, optimal algorithms in emergent computation, the extremal principle and its applications, turnpike property for variational problems, asymptotic behavior of random infinite products of some operators, inequalities for Riemann-Stieltjes integral. Other topics covered include nonsmooth analysis and analysis of linear operators and set-valued mappings, numerical methods and generalized penalty functions, applied optimal control problems and Markov decision processes, optimal estimation of signal parameters and the problem of maximal time congestion.
Audience: Specialists in optimization, mathematical programming, convex analysis, nonsmoooth analysis, engineers using mathematical tools and optimization technique, specialists in mathematical modeling.
Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
An Approach to Constructing Generalized Penalty Functions....Pages 3-14
An Exact Method for Solving the Subproblem of the Cutting Angle Method of Global Optimization....Pages 15-26
On Modeling Risk in Markov Decision Processes....Pages 27-40
Multiplicative Programming and beyond Via C-Programming....Pages 41-60
Computing Optimal Control on MATLAB — The SCOM Package and Economic Growth Models....Pages 61-70
Stochastic Optimal Control of a Solar Car....Pages 71-81
On Optimal Algorithms in Emergent Computation....Pages 83-102
Optimal Estimation of Signal Parameters Using Bilinear Observations....Pages 103-117
On an Extremal Problem Arising in Queueing Theory and Telecommunications....Pages 119-134
Level Functions of Some Optimal Value Functions....Pages 135-152
Regularized Gap Functions and D-Gap Functions for Nonsmooth Variational Inequalities....Pages 153-176
Front Matter....Pages 177-177
Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance....Pages 179-196
Some Inequalities for Riemann-Stieltjes Integral and Applications....Pages 197-235
Prox-Regularity and Subjets....Pages 237-313
Concerning Differentiability Properties of Locally Lipschitz Functions....Pages 315-323
Laurent Series for the Inversion of Perturbed Linear Operators on Hilbert Space....Pages 325-342
The Extremal Principle and its Applications to Optimization and Economics....Pages 343-369
Generic Convergence of Infinite Products of Nonexpansive Mappings in Banach and Hyperbolic Spaces....Pages 371-402
Recession Cones of Star-Shaped and Co-Star-Shaped Sets....Pages 403-414
Does Continuity of Convex-Valued Maps Survive Under Intersection?....Pages 415-428
Back Matter....Pages 459-461
Existence and Structure of Solutions of Optimal Control Problems....Pages 429-457

---

The book, comprised predominantly of survey chapters, is a collection of recent results in various fields of theoretical and applied optimization and related topics. It contains survey papers on second order nonsmooth analysis, based on subjects, multiplicative programs and c-programming, optimal algorithms in emergent computation, the extremal principle and its applications, turnpike property for variational problems, asymptotic behavior of random infinite products of some operators, inequalities for Riemann-Stieltjes integral. Other topics covered include nonsmooth analysis and analysis of linear operators and set-valued mappings, numerical methods and generalized penalty functions, applied optimal control problems and Markov decision processes, optimal estimation of signal parameters and the problem of maximal time congestion.
Audience: Specialists in optimization, mathematical programming, convex analysis, nonsmoooth analysis, engineers using mathematical tools and optimization technique, specialists in mathematical modeling.
Content:
Front Matter....Pages i-xiv
Front Matter....Pages 1-1
An Approach to Constructing Generalized Penalty Functions....Pages 3-14
An Exact Method for Solving the Subproblem of the Cutting Angle Method of Global Optimization....Pages 15-26
On Modeling Risk in Markov Decision Processes....Pages 27-40
Multiplicative Programming and beyond Via C-Programming....Pages 41-60
Computing Optimal Control on MATLAB — The SCOM Package and Economic Growth Models....Pages 61-70
Stochastic Optimal Control of a Solar Car....Pages 71-81
On Optimal Algorithms in Emergent Computation....Pages 83-102
Optimal Estimation of Signal Parameters Using Bilinear Observations....Pages 103-117
On an Extremal Problem Arising in Queueing Theory and Telecommunications....Pages 119-134
Level Functions of Some Optimal Value Functions....Pages 135-152
Regularized Gap Functions and D-Gap Functions for Nonsmooth Variational Inequalities....Pages 153-176
Front Matter....Pages 177-177
Convex Spectral Functions of Compact Operators, Part II: Lower Semicontinuity and Rearrangement Invariance....Pages 179-196
Some Inequalities for Riemann-Stieltjes Integral and Applications....Pages 197-235
Prox-Regularity and Subjets....Pages 237-313
Concerning Differentiability Properties of Locally Lipschitz Functions....Pages 315-323
Laurent Series for the Inversion of Perturbed Linear Operators on Hilbert Space....Pages 325-342
The Extremal Principle and its Applications to Optimization and Economics....Pages 343-369
Generic Convergence of Infinite Products of Nonexpansive Mappings in Banach and Hyperbolic Spaces....Pages 371-402
Recession Cones of Star-Shaped and Co-Star-Shaped Sets....Pages 403-414
Does Continuity of Convex-Valued Maps Survive Under Intersection?....Pages 415-428
Back Matter....Pages 459-461
Existence and Structure of Solutions of Optimal Control Problems....Pages 429-457
....