The work by Gould, Loh, and Robinson [SIAM J. Optim., 24 (2014), pp. 175–209] established global convergence of a new filter line search method for finding local first-order solutions to nonlinear and nonconvex constrained optimization problems. A key contribution of that work was that the search direction was computed using the same procedure during every iteration from subproblems that were a...

This paper extends the derivative-free descent method [18] for the nonlinear complementarity problem to the symmetric cone complementarity problem (SCCP). The algorithm is based on the unconstrained implicit Lagrangian reformulation of the SCCP, but uses a convex combination of the negative partial gradients of the implicit Lagrangian function ψα, i.e. the vector of the form −θ∇xψα −(1 −θ)∇yψα ...

A Greedy Randomized Adaptive Search Procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con...

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Abstract This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points unconstrained and boxed constrained mixed-integer optimization problems. A new concept is introduced: the quasi-descent direction. point x on set search directions if there exists no feasible qdd set. The method does not require computation derivatives nor explicit manipulation asymptoti...

The steepest descent method proposed by Fliege and Svaiter has motivated the research on methods for multiobjective optimization, which received increasing attention in recent years. However, empirical results show that Armijo line search often a very small stepsize along direction, decelerates convergence seriously. This paper points out issue is mainly due to imbalances among objective functi...

Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow ...

This paper presents a derivative-free nonmonotone hybrid tabu search to compute a solution of overdetermined systems of inequalities and equalities through the global optimization of an appropriate merit function. The proposed algorithm combines global and local searches aiming to reduce computational effort. Preliminary numerical results show the effectiveness of the combined heuristic.

The negative gradient direction to find local minimizers has been associated with the classical steepest descent method which behaves poorly except for very well conditioned problems. We stress out that the poor behavior of the steepest descent methods is due to the optimal Cauchy choice of steplength and not to the choice of the search direction. We discuss over and under relaxation of the opt...