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This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneous of degree one to within a constant. Two rather general auxiliary problems are developed, and the relations between the solutions of the auxiliary problems and the solutions of the original problem are codified. Applications of the results for specific problems are also presented. [ABSTRACT FROM AUTHOR]

This paper describes a two-person zero-sum game in function space concerning the optimal allocation of a homogenous defense force on different levels of readiness. The second player, the attacker, wants to determine the time for the attack such that the cost is minimized. As the defense is subject to attrition, a delay is preferable for the attacker. This is balanced, however, by a delay cost which increases with time. The existence of a solution consisting of a pure defense strategy and a mixed strategy for the attack time is proved elsewhere. This paper mainly treats an approximation of the game with a time-discrete version for which an algorithm is derived. Arbitrarily close upper and lower bounds of the value of the original game can be obtained by the algorithm, as well as feasible defense and attacker strategies that realize these value estimates. Computational results are given for two simple problems, one of which is also solved analytically. [ABSTRACT FROM AUTHOR]

This paper is concerned with showing differentiability and measure theoretic properties on demand functions. The main results are roughly as follows. (i) Demand is differentiable and the Slutsky equation holds for almost all prices if demand satisfies a Lipschitz condition in income (except possibly for a closed cone of prices of measure zero) and utility is concave. This includes the homothetic case which is given special attention in Section 4. (ii) For the Slutsky equation to indicate demand behavior in the large, it is sufficient that along any given indifference curve the ratio of changes in price to changes in quantity be bounded from zero (Section 5). (iii) Even with almost everywhere differentiable demand derived from continuously differentiable utility, most change in demand does not necessarily take place where the Slutsky equation is valid (Section 5). (iv) By way of proof of Theorems 1-3, it is shown that the maximand in a Lagrange problem is differentiable under appropriate conditions on the function being maximized (Theorem 6, Section 3, and Appendix). (v) For preferences as in (ii) and for almost all wealths, equilibrium is locally unique (Section 6). [ABSTRACT FROM AUTHOR]

It comments on a paper by W. Eichhorn and W. Oettli which proved a theorem concerning a real-valued functional defined on the Cartesian product A × B of two sets A and B. The paper suggests that certain conditions in the theorem are unnecessarily restrictive. The content of the modified theorem may be displayed by considering the stronger form (with ⑤ replaced by <) and regarding F(x, λ) as a cost linked with a process x and depending also on a parameter < that varies with time.