User's Guide for FSQP Version 2.0 A Fortran Code for Solving Optimization Problems, Possibly Minimax, with General Inequality Constraints and Linear Equality Constraints, Generating Feasible Iterates

Abstract

FSQP 2.0 is a set of Fortran subroutines for the minimization of the maximum of a set of smooth objective functions (possibly a single one) subject to nonlinear smooth inequality constraints, linear inequality and linear equality constraints, and simple bounds on the variables. If the initial guess provided by the user is infeasible, FSQP first generates a feasible point; subsequently the successive iterates generated by FSQP all satisfy the constraints. The user has the option of requiring that the maximum value among the objective functions decrease at each iteration after feasibility has been reached (monotone line search). He/She must provide subroutines that define the objective functions and constraint functions and may either provide subroutines to compute the gradients of these functions or require that FSQP estimate them by forward finite differences. FSQP 2.0 implements two algorithms based on Sequential Quadratic Programming (SQP), modified so as to generate feasible iterates. In the first one (monotone line search), a certain Armijo type arc search is used with the property that the step of one is eventually accepted, a requirement for superlinear convergence. In the second one the same effect is achieved by means of a (nonmonotone) search along a straight line. The merit function used in both searches is the maximum of a objective functions.