Search

The linear complementarity problem and the piecewise linear system are the two principal models in complementary pivot and fixed point theory. It is shown that the path following methods for solving each are conceptually equivalent. (Author), Sponsored in part by Grant NSF-MCS78-02096.

An algorithm for a piecewise linear model of trade and production with negative prices and bankruptcy is described. The algorithm uses complementary pivoting to adjust the utility weights as in welfare economics and generates an approximate equilibrium or demonstrates that the traders are not resource related. (Author)

Society could benefit greatly if certain total systems can be modeled and successfully solved. For example, crude economic planning models of many developing countries indicate a potential growth rate of GNP of 10% to 15% per year. To implement such a growth requires carefully worked-out detailed models and the availability of computer programs that can solve the resulting large- scale systems. The world is also faced with difficult problems related to population growth, availability of natural resources, ecological evaluation and control, urban redesign, design of large-scale engineering systems (e.g., atomic energy and recycling systems) and the modeling of man's physiological system for diagnosis and treatment. These problems are complex, are urgent and can only be solved if viewed as total systems. The paper will review progress to date, the various techniques that have been proposed, and the need to set-up large-scale system optimization laboratories where the different techniques can be tested on representative problems., Sponsored in part by National Science Foundation, Grant NSF-GP-31393.