SIAM Journal on Control and Optimization
On combining feasibility, descent and superlinear convergence in inequality constrained optimization
Mathematical Programming: Series A and B
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
SIAM Journal on Optimization
An Algorithm for the Inequality-Constrained Discrete Min--Max Problem
SIAM Journal on Optimization
Pseudospectral Components and the Distance to Uncontrollability
SIAM Journal on Matrix Analysis and Applications
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
Convergence of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization
SIAM Journal on Optimization
A Nonderivative Version of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization
SIAM Journal on Optimization
A feasible directions method for nonsmooth convex optimization
Structural and Multidisciplinary Optimization
A line search exact penalty method using steering rules
Mathematical Programming: Series A and B
An adaptive gradient sampling algorithm for non-smooth optimization
Optimization Methods & Software
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The gradient sampling (GS) algorithm for minimizing a nonconvex, nonsmooth function was proposed by Burke et al. (SIAM J Optim 15:751---779, 2005), whose most interesting feature is the use of randomly sampled gradients instead of subgradients. In this paper, combining the GS technique with the sequential quadratic programming (SQP) method, we present a feasible SQP-GS algorithm that extends the GS algorithm to nonconvex, nonsmooth constrained optimization. The proposed algorithm generates a sequence of feasible iterates, and guarantees that the objective function is monotonically decreasing. Global convergence is proved in the sense that, with probability one, every cluster point of the iterative sequence is stationary for the improvement function. Finally, some preliminary numerical results show that the proposed algorithm is effective.