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Abstract: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [Copyright &y& Elsevier]

Abstract: A directed searching optimization algorithm (DSO) is proposed to solve constrained optimization problems in this paper. The proposed algorithm includes two important operations — position updating and genetic mutation. Position updating enables the non-best solution vectors to mimic the best one, which is beneficial to the convergence of the DSO; genetic mutation can increase the diversity of individuals, which is beneficial to preventing the premature convergence of the DSO. In addition, we adopt the penalty function method to balance objective and constraint violations. We can obtain satisfactory solutions for constrained optimization problems by combining the DSO and the penalty function method. Experimental results indicate that the proposed algorithm can be an efficient alternative on solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: In image restoration, the so-called edge-preserving regularization method is used to solve an optimization problem whose objective function has a data fidelity term and a regularization term, the two terms are balanced by a parameter . In some aspect, the value of determines the quality of images. In this paper, we establish a new model to estimate the parameter and propose an algorithm to solve the problem. In order to improve the quality of images, in our algorithm, an image is divided into some blocks. On each block, a corresponding value of has to be determined. Numerical experiments are reported which show efficiency of our method. [Copyright &y& Elsevier]

Abstract: In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. [Copyright &y& Elsevier]