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Most of the fractures of engineering structures are due to fatigue and the consequences are disastrous. How to envisage in what operational lifetime fatigue failure would occur, i.e. how to assess the fatigue life, has been one of the most important engineering problems for the last two centuries. There was not any uniform and all-acknowledged solution under any loading including the general multiaxial case of non-proportional, non-cyclic and arbitrary wave-forms of the stress components. According to this book, the lack of solution was for the fatigue life had not been searched for by means...

In this book, the theory, methods and applications of separable optimization are considered. Some general results are presented, techniques of approximating the separable problem by linear programming problem, and dynamic programming are also studied. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and convergent iterative algorithms of polynomial complexity are proposed.  As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. The problems of...