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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: Last few years have witnessed the development of various multi-objective evolutionary algorithms since they allow the generation of the overall Pareto front for multi-objective optimizations. With the problems in the real-world becoming more and more complex, however, no reported work in the literature focuses on the high-dimensional objective optimizations (HOPs). In this paper, we propose an evolutionary algorithm named HOEA (high-dimensional objective evolutionary algorithm) for HOPs. By adopting the concept of nonlinear definition for optimizing object, HOPs can be solved by HOEA, while the well-known multi-objective evolutionary algorithms work poorly on HOPs. We further analyze the nonlinear dynamic properties of HOEA on the basis of martingale theoretical framework. The theoretical results indicate that this new algorithm is indeed capable of achieving convergence. We also conduct experiments on HOEA with two representative test instances. The experimental results either confirm our theoretical results or show that the proposed algorithm is efficient and effective for HOPs. [Copyright &y& Elsevier]

Abstract: In this paper, by means of a new efficient identification technique of active constraints and the method of strongly sub-feasible direction, we propose a new sequential system of linear equations (SSLE) algorithm for solving inequality constrained optimization problems, in which the initial point is arbitrary. At each iteration, we first yield the working set by a pivoting operation and a generalized projection; then, three or four reduced linear equations with a same coefficient are solved to obtain the search direction. After a finite number of iterations, the algorithm can produced a feasible iteration point, and it becomes the method of feasible directions. Moreover, after finitely many iterations, the working set becomes independent of the iterates and is essentially the same as the active set of the KKT point. Under some mild conditions, the proposed algorithm is proved to be globally, strongly and superlinearly convergent. Finally, some preliminary numerical experiments are reported to show that the algorithm is practicable and effective. [Copyright &y& Elsevier]

Abstract: In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods. [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]