It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the implementation are derived from scratc...

Mathematical programs with nonlinear complementarity constraints are refor-mulated using better-posed but nonsmooth constraints. We introduce a class offunctions, parameterized by a real scalar, to approximate these nonsmooth prob-lems by smooth nonlinear programs. This smoothing procedure has the extrabenefits that it often improves the prospect of feasibility and stability...

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding th...

Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show t...

The aim of the present study is to a new model based on nonlinear singular second order delay differential equation Lane–Emden type and numerically solved by using heuristic technique. Four different examples are presented designed artificial neural networks optimized global search, local search methods their hybrid combinations, respectively, named as genetic algorithm (GA), sequential quadrat...

We present the first bioluminescence tomography algorithm that makes use of the PDEconstrained concept, which has shown to lead to significant savings in computation times in similar applications. Implementing a sequential quadratic programming (SQP) method, we solve the forward and inverse problems simultaneously. Using numerical results we show that the PDEconstrained SQP approach leads to ~1...

We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterate genera...

Sequential quadratic programming (SQP) methods for nonlinearly constrained optimization typically use a merit function to enforce convergence from an arbitrary starting point. We define a smooth augmented Lagrangian merit function in which the Lagrange multiplier estimate is treated as a separate variable, and inequality constraints are handled by means of non-negative slack variables that are ...

Sequential quadratic programming (SQP) methods are widely used for solving practical optimization problems, especially in structural mechanics. The general structure of SQP methods is briefly introduced and it is shown how these methods can be adapted to distributed computing. However, SQP methods are sensitive subject to errors in function and gradient evaluations. Typically they break down wi...

In this paper, an integration of Improve Particle Swarm Optimization (IPSO) in combination with Successive Quadratic programming (SQP) so called IPSO-SQP algorithm is proposed to solve time optimal bang-bang control problems. The procedure is found not sensitive to the initial guess of the solution. Due to random selection in the first stage of the search process, the chance of converging to th...