The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi- ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe- matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the...

The clearest way into the Universe is through a forest wilderness. John MuIr As recently as 1970 the problem of obtaining optimal estimates for variance components in a mixed linear model with unbalanced data was considered a miasma of competing, generally weakly motivated estimators, with few firm gUidelines and many simple, compelling but Unanswered questions. Then in 1971 two significant beachheads were secured: the results of Rao 1971a, 1971b] and his MINQUE estimators, and related to these but not originally derived from them, the results of Seely 1971] obtained as part of his...

The book of Professor Evtushenko describes both the theoretical foundations and the range of applications of many important methods for solving nonlinear programs. Particularly emphasized is their use for the solution of optimal control problems for ordinary differential equations. These methods were instrumented in a library of programs for an interactive system (DISO) at the Computing Center of the USSR Academy of Sciences, which can be used to solve a given complicated problem by a combination of appropriate methods in the interactive mode. Many examples show the strong as well the weak...

Of recent coinage, the term "nondifferentiable optimization" (NDO) covers a spectrum of problems related to finding extremal values of nondifferentiable functions. Problems of minimizing nonsmooth functions arise in engineering applications as well as in mathematics proper. The Chebyshev approximation problem is an ample illustration of this. Without loss of generality, we shall consider only minimization problems. Among nonsmooth minimization problems, minimax problems and convex problems have been studied extensively ( 31], 36], 57], 110], 120]). Interest in NDO has been constantly...