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In this paper, a novel hybrid lightning search algorithm-simplex method (LSA-SM) is proposed to solve the shortcomings of lightning search algorithm (LSA) premature convergence and low computational accuracy and it is applied to function optimization and constrained engineering design optimization problems. The improvement adds two major optimization strategies. Simplex method (SM) iteratively optimizes the current worst step leaders to avoid the population searching at the edge, thus improving the convergence accuracy and rate of the algorithm. Elite opposition-based learning (EOBL) increases the diversity of population to avoid the algorithm falling into local optimum. LSA-SM is tested by 18 benchmark functions and five constrained engineering design problems. The results show that LSA-SM has higher computational accuracy, faster convergence rate, and stronger stability than other algorithms and can effectively solve the problem of constrained nonlinear optimization in reality. [ABSTRACT FROM AUTHOR]

This paper develops a particle swarm optimization (PSO) based framework for constrained optimization problems (COPs). Aiming at enhancing the performance of PSO, a modified PSO algorithm, named SASPSO 2011, is proposed by adding a newly developed self-adaptive strategy to the standard particle swarm optimization 2011 (SPSO 2011) algorithm. Since the convergence of PSO is of great importance and significantly influences the performance of PSO, this paper first theoretically investigates the convergence of SASPSO 2011. Then, a parameter selection principle guaranteeing the convergence of SASPSO 2011 is provided. Subsequently, a SASPSO 2011-based framework is established to solve COPs. Attempting to increase the diversity of solutions and decrease optimization difficulties, the adaptive relaxation method, which is combined with the feasibility-based rule, is applied to handle constraints of COPs and evaluate candidate solutions in the developed framework. Finally, the proposed method is verified through 4 benchmark test functions and 2 real-world engineering problems against six PSO variants and some well-known methods proposed in the literature. Simulation results confirm that the proposed method is highly competitive in terms of the solution quality and can be considered as a vital alternative to solve COPs. [ABSTRACT FROM AUTHOR]

A practical algorithm for solving large-scale box-constrained optimization problems is developed, analyzed, and tested. In the proposed algorithm, an identification strategy is involved to estimate the active set at per-iteration. The components of inactive variables are determined by the steepest descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method--L-BFGS-B. [ABSTRACT FROM AUTHOR]

A line search filter SQPmethod for inequality constrained optimization is presented. This method makes use of a backtracking line search procedure to generate step size and the efficiency of the filter technique to determine step acceptance. At each iteration, the subproblemis always consistent, and it only needs to solve oneQPsubproblem. Under some mild conditions, the global convergence property can be guaranteed. In the end, numerical experiments show that the method in this paper is effective. [ABSTRACT FROM AUTHOR]

Motivated by the method of Su and Pu (2009), we present an improved nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. In our algorithmamodified nonmonotone filter technique is proposed and the restoration phase is not needed. At every iteration, in common with the composite-step SQP methods, the step is viewed as the sum of two distinct components, a quasinormal step and a tangential step. Amore relaxed accepted condition for trial step is given and a crucial criterion is weakened. Under some suitable conditions, the global convergence is established. In the end, numerical results show our method is effective. [ABSTRACT FROM AUTHOR]

A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method.We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method. [ABSTRACT FROM AUTHOR]