Nonlinear Programming: Algorithms, Software, and Applications

Abstract

A b s t r a c tWe introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The methods are outlined in a uniform way and the results of some comparative performance tests are listed. We especially show the suitability of sequential convex programming methods to solve some classes of very large scale nonlinear programs, where implicitly defined systems of equations seem to support the usage of inverse approximations. The areas of interest are structural mechanical optimization, i.e., topology optimization, and optimal control of partial differential equations after a full discretization. In addition, a few industrial applications and case studies are shown to illustrate practical situations under which the codes implemented by the authors are in use.

Crushing analysis and crashworthiness optimization design of reinforced regular hexagon honeycomb sandwich panel

“…In addition, researches of Schittkowski and Zillober [54] had proved that the functions and gradients of NLPQL must be provided by reverse communication. Moreover, this algorithm is executed with termination accuracy 10 -8 , and the maximum number of iterations is 500.…”

Analysis of inhomogeneous stress distribution in surface acoustic wave resonator

“…Another assumption is that it is possible to cascade the period, i.e. that there is no wave polarization change from one transducer section to the other and that it is possible to assume that the output wave amplitude for one section is the input wave amplitude for the neighboring section [1].…”

Anti-Lock Braking System Using Predictive Control and On-Line Tire/Road Characteristics Estimation

“…The minimization of such a problem can be achieved by the use a Quasi-Newton SQP algorithm. More information on numerical optimization can be found in (Bonnans et al, 2003;Schittkowski and Zillober, 2004) and a practical implementation of a robust SQP algorithm is given in (Liu and Yuan, 2000).…”