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For constrained equations with nonisolated solutions, we show that if the equation mapping is 2-regular at a given solution with respect to a direction in the null space of the Jacobian, and this direction is interior feasible, then there is an associated domain of starting points from which a family of Newton-type methods is well defined and necessarily converges to this specific solution (despite degeneracy, and despite that there are other solutions nearby). We note that unlike the common settings of convergence analyses, our assumptions subsume that a local Lipschitzian error bound does not hold for the solution in question. Our results apply to constrained and projected variants of the Gauss-Newton, Levenberg-Marquardt, and LP-Newton methods. Applications to smooth and piecewise smooth reformulations of complementarity problems are also discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we adapt a genetic algorithm for constrained optimization problems. We use a dynamic penalty approach along with some form of annealing, thus forcing the search to concentrate on feasible solutions as the algorithm progresses. We suggest two different general-purpose methods for guaranteeing convergence to a globally optimal (feasible) solution, neither of which makes any assumptions on the structure of the optimization problem. The former involves modifying the GA evolution operators to yield a Boltzmann-type distribution on populations. The latter incorporates a dynamic penalty along with a slow annealing of acceptance probabilities. We prove that, with probability one, both of these methods will converge to a globally optimal feasible state. [ABSTRACT FROM AUTHOR]

In this note, we prove that the convergence results for vector optimization problems with equilibrium constraints presented in Wu and Cheng (J. Optim. Theory Appl. 125, 453–472, 2005) are not correct. Actually, we show that results of this type cannot be established at all. This is due to the possible lack, even under nice assumptions, of lower convergence of the solution map for equilibrium problems, already deeply investigated in Loridan and Morgan (Optimization 20, 819–836, 1989) and Lignola and Morgan (J. Optim. Theory Appl. 93, 575–596, 1997). [ABSTRACT FROM AUTHOR]