FACTUNC:: a user-friendly system for unconstrained optimization

FACTUNC is a system for solving unconstrained minimization problems based on the concept of factorable programming. This concept enables the user to provide the problem function and data in a user friendly way and does not require user-supplied derivatives. The system utilizes the factorable function concept to obtain the first and second derivatives required for unconstrained optimization. In all cases derivatives are obtained rapidly and accurately (up to roundoff errors due to machine precision) , as opposed to finite differencing. As a system for nonlinear minimization, FACTUNC allows several options. First the user can solve regression (nonlinear least squares) problems by providing the regression equation and the data for the dependent and independent variables. The second option allows for the minimization of the sum of an indexed function. The user provides the function, and the indexed data. This can be used for example to solve maximum likelihood estimation problems when the user provides the negative of the (weighted) log of the frequency function and the data. The third option is simply to minimize a function supplied by the user. Utilizing barrier function methodology, this third option can sometimes be used to solve constrained problems. TABLE OF CONTENTS 1 . Introduction 1 . 1 Representation of Functions in FACTUNC 2. Mathematical Background on Factorable Functions 3. Solving Regression (Least Squares) Problems (Option 1) EXAMPLE: SMOKING AND HEALTH 4. Minimizing the Sum of an Indexed Function (Option 2) 4.1 Maximum Likelihood Estimation EXAMPLE: SYSTOLIC BLOOD PRESSURE 5. Minimizing a General Unconstrained Function (Option 3) 5.1 Solving Constrained Problems via Unconstrained Optimization EXAMPLE: CHEMICAL EQUILIBRIUM 6 . Future Work 7. References APPENDIX A: Abbreviated Output APPENDIX B: Abbreviated Output APPENDIX C: Abbreviated Output for MAXL Option Example for Chemical Equilibrium Problem for Chemical Equilibrium Problem (r,=.01)