FSQP

nonlinear and minmax constrained optimization, with feasible iterates

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FSQP consists of two packages: FFSQP (FORTRAN) and CFSQP (C). The algorithms in FSQP are based on the concept of feasible sequential quadratic programming. For problems without nonlinear equality constraints, starting with a feasible point (provided by the user or generated automatically) these algorithms produce successive iterates that all satisfy the constraints. After feasibility has been reached, the objective function can be decreased either after each iteration with an Armijo-type arc search or after at most three iterations with a nonmonotone line search. The user has the option to choose one of the two searches. The merit function used in both searches is the objective function itself. Equality constraints are handled by way of an exact, differentiable penalty function that penalizes negative values, while positive values are precluded by the same scheme used for inequality constraints. In addition, CFSQP includes a special scheme for efficiently handling problems with many more objectives or constraints than variables (e.g., finely discretized semi-infinite problems).

Both algorithms in FSQP can be shown to have global and two-step superlinear convergence properties. The user can provide routines for gradients of objective and constraint functions or require that gradients be computed by finite differences. An interface between FFSQP and ADIFOR (automatic differentiation) is also available.

FFSQP is written in ANSI Fortran 77; CFSQP is written in C and complies with both ANSI and K&R rules. The packages include test problems and detailed user's guides. They are available free of charge to non-profit organizations.

Need more info?

Visit the FSQP Home Page or contact

 
 ,
Prof. Andre L. Tits 
Dept. of Electrical Engineering and
Institute for Systems Research 
University of Maryland
College Park, MD 20742 
Phone: (301) 405-3669 
Fax: (301) 405-6707 
E-Mail: andre@isr.umd.edu

References:

J. F. Bonnans, E. R. Panier, A. L. Tits, and J. L. Zhou, Avoiding the Maratos effect by means of a nonmonotone line search. II: Inequality constrained problems -- feasible iterates, SIAM J. Numer. Anal. 29 (1992), pp. 1187--1202.

E. R. Panier and A.L. Tits, On combining feasibility, descent and superlinear convergence in inequality constrained optimization, Math. Programming 59 (1993), pp. 261--276.

J. L. Zhou and A. L. Tits, Nonmonotone line search for minimax problems, J. Optim. Theory Appl. 76 (1993), pp. 455--476.

J.L. Zhou and A.L. Tits, An SQP Algorithm for Finely Discretized Continuous Minimax Problems and Other Minimax Problems with Many Objective Functions, SIAM J. on Optimization, vol. 6, No. 2, 1996, pp. 461--487.

J. L. Zhou and A. L. Tits, User's Guide for FFSQP Version 3.5 --- A FORTRAN Code for Solving Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints, Institute for Systems Research, University of Maryland, 1995.

C.T. Lawrence, J.L. Zhou and A.L. Tits,User's Guide for CFSQP Version 2.3: A C Code for Solving (Large Scale) Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints, Institute for Systems Research, College Park, Maryland, 1995.

C.T. Lawrence and A.L. Tits, Nonlinear Equality Constraints in Feasible Sequential Quadratic Programming, Optimization Methods and Software, vol. 6, pp. 265-282, March 1996.

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