Sharif Digital Repository

We present a competitive algorithm to minimize a locally Lipschitz function constrained with locally Lipschitz constraints. The approach is to use an ℓ1 nonsmooth penalty function. The method generates second order descent directions to minimize the ℓ1 penalty function. We introduce a new criterion to decide upon acceptability of a Goldstein subdifferential approximation. We show that the new criterion leads to an improvement of the Goldstein subdifferential approximation, as introduced by Mahdavi-Amiri and Yousefpour. Also, making use of our proposed line search strategy, the method always moves on differentiable points. Furthermore, the method has an adaptive behaviour in the sense that,... 

We present a competitive algorithm to minimize a locally Lipschitz function constrained with locally Lipschitz constraints. The approach is to use an ℓ1 nonsmooth penalty function. The method generates second order descent directions to minimize the ℓ1 penalty function. We introduce a new criterion to decide upon acceptability of a Goldstein subdifferential approximation. We show that the new criterion leads to an improvement of the Goldstein subdifferential approximation, as introduced by Mahdavi-Amiri and Yousefpour. Also, making use of our proposed line search strategy, the method always moves on differentiable points. Furthermore, the method has an adaptive behaviour in the sense that,... 

A new method for structural optimization is presented for successive approximation of the objective function and constraints in conjunction with Lagrange multipliers approach. The focus is on presenting the methodology with simple examples. The basis of the iterative algorithm is that after each iteration, it brings the approximate location of the estimated minimum closer to the exact location, gradually. In other words, instead of the linear or parabolic term used in Taylor expansion, which works based on a short step length, an arch is used that has a constant curvature but a longer step length. Using this approximation, the equations of optimization involve the Lagrange multipliers as the... 

Optimizing highway alignment requires a versatile set of cost functions and an efficient search method to achieve the best design. Because of numerous highway design considerations, this issue is classified as a constrained problem. Moreover, because of the infinite number of possible solutions for the problem and the continuous search space, highway alignment optimization is a complex problem. In this study, a customized particle swarm optimization algorithm was used to search for a near-optimal highway alignment, which is a compound of several tangents, consisting of circular (for horizontal design) and parabolic (for vertical alignment) curves. The selected highway alignment should meet... 

New penalty functions, which have better convergence properties, as compared to the commonly used exterior and interior penalty functions, have been proposed in this paper. The convergence behavior and accuracy of ordinary penalty functions depend on the selection of appropriate penalty parameters. The optimization of ordinary penalty functions is accomplished after several rounds of optimization where, at each round a different but fixed value of penalty parameter is used. While some useful hints and rules for the selection of suitable penalty parameter values have been provided by different authors, the objective of this paper has been to improve this procedure by including the penalty...