CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search
Journal of Global Optimization
A bundle-filter method for nonsmooth convex constrained optimization
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Steering exact penalty methods for nonlinear programming
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
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The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.