Feasible Sequential Quadratic Programming For Finely Discretized Problems From Sip

A Sequential Quadratic Programming algorithm designed to efficiently solve nonlinear optimization problems with many inequality constraints, e.g. problems arising from finely discretized Semi-Infinite Programming, is described and analyzed. The key features of the algorithm are (i) that only a few of the constraints are used in the QP sub-problems at each iteration, and (ii) that every iterate satisfies all constraints. 1 INTRODUCTION Consider the Semi-Infinite Programming (SIP) problem minimize f(x) subject to \Phi(x) 0; (SI) where f : IR n ! IR is continuously differentiable, and \Phi : IR n ! IR is defined by \Phi(x) \Delta = sup ¸2[0;1] OE(x; ¸); with OE : IR n \Theta [0; 1] ! IR continuously differentiable in the first argument. For an excellent survey of the theory behind the problem (SI), in addition to some algorithms and applications, see [9] as well as the other papers in the present volume. Many globally convergent algorithms designed to solve (SI) 2 Chapter 1..

Optimum blank design by the predictor-corrector scheme of SLM and FSQP in the deep drawing process of square cup with flange

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SQP methods for large-scale nonlinear programming

We compare and contrast a number of recent sequential quadratic programming (SQP) methods that have been proposed for the solution of large-scale nonlinear programming problems. Both line-search and trust-region approaches are considered, as are the implications of interior-point and quadratic programming methods