Synopses & Reviews
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.
Table of Contents
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.