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In this paper, we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper, we establish the exact penalty property for a large class of inequality-constrained minimization problems. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive penalty function for solving constrained optimization problems using genetic algorithms. The proposed method aims to exploit infeasible individuals with low objective value and low constraint violation. The number of feasible individuals in the population is used to guide the search process either toward finding more feasible individuals or searching for the optimum solution. The proposed method is simple to implement and does not need any parameter tuning. The performance of the algorithm is tested on 22 benchmark functions in the literature. The results show that the proposed approach is able to find very good solutions comparable to the chosen state-of-the-art designs. Furthermore, it is able to find feasible solutions in every run for all of the benchmark functions tested. [ABSTRACT FROM AUTHOR]

In this paper, a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed. The class is defined by any positive potential function describing the contour interior characterization. An evolutionary strategy is used to derive the algorithm. A similarity threshold Tv can be used to determine the interior size and shape of the contour. Sensitivity and significance of Tv and σ (a spreadness measure) are also discussed and shown. Experiments on noisy images and the convergence to a minimum energy gap contour are included. The developed method has been applied to a variety of medical images from CT abdominal section, MRI image slices of brain, brain tumor, a pig heart ultrasound image sequence to visual blood cell images. As the results show, the algorithm can be adapted to a broad range of medical images containing objects with vague, complex and/or irregular shape boundary, inhomogeneous and noisy interior, and contour with small gaps. [ABSTRACT FROM AUTHOR]

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 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]