Decomposition in Fixed Point Computation.
STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB
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One result of this paper is the most efficient complementary pivot algorithm to date for handling the optimization problem. The second major contribution is a general structure on fixed point problems which, when present, enables one to work in a lower dimensional space. It is shown that the general constrained optimization problem may sometimes be formulated as a fixed point problem possessing this property. The basic approach adopted in this work for handling the general constrained optimization problem is to use an implicit function derived from the equality constraints to solve for some dependent variables in terms of the remaining independent ones. Under certain circumstances, a fixed point algorithm may be used to search for optimal values of the independent variables while Newtons method is used to determine values of the dependent variables. Theoretical conditions on the original functions are developed to guarantee that the fixed point algorithm converges to a solution and various techniques are devised to enhance the overall efficiency.
- Theoretical Mathematics
- Operations Research