In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behi...
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In the context of sequential methods for solving general nonlinear programming problems, it is usual to work with augmented subproblems instead of the original ones. This paper addresses the theoretical reasoning behind handling the original subproblems by an augmentation strategy related to the differentiable reformulation of the-penalized problem. Nevertheless, this paper is not concerned with the sequential method itself, but with the features about the original problem that can be inferred from the properties of the solution of the augmented problem. Moreover, no assumption is made upon the feasibility of the original problem, neither about the fulfillment of any constraint qualification, nor of any regularity condition, such as calmness. The convergence analysis of the involved sequences is presented, independent of the strategy employed to produce the iterates. Examples that elucidate the interrelations among the obtained results are also provided.
The focus of this work is on analyzing and developing nonlinear solvers for performing nonlinear structural analysis for large displacements in both elastic and inelastic cases. The response of a structure to a load a...
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The focus of this work is on analyzing and developing nonlinear solvers for performing nonlinear structural analysis for large displacements in both elastic and inelastic cases. The response of a structure to a load application is shown by its equilibrium path which may include snap back and snap through behavior. Material and geometric nonlinearities are taken into consideration while developing the response path of a multi-element structure with sections discretized using fiber elements. Traditionally, Newton’s method is employed for solving the system of nonlinear equations but it comes with certain challenges. The response determination becomes difficult when stiffness matrix becomes singular at turning point. It also requires the calculation of the inverse of a Hessian matrix, which is costly. Newton’s method gives quadratic convergence but as the scale of the structure increases, resorting to Newton’s method becomes *** limitations motivate us to explore new solvers. Hence, in this study we analyze and develop various nonlinearly constrained optimization solvers for a recently suggested hybrid finite element. In particular, we compare the performance of conjugate gradient method with or without preconditioning, Sequential Quadratic programming method and augmented Lagrangian method. For the case of structural response with snap back and snap through behavior, a new method called the implicit path continuation method is developed to ensure path continuation and solution convergence. The various solvers are then validated by obtaining responses of three benchmark structural problems with large displacements and rotations, and comparing the results with the conventional Newton’s method and a variant of Newton’s method with submatrices.
A simple and efficient method for eliminating branch overloads in power systems is presented in this paper. The overloads are eliminated by corrective control actions, which are computed by an efficient and accurate n...
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A simple and efficient method for eliminating branch overloads in power systems is presented in this paper. The overloads are eliminated by corrective control actions, which are computed by an efficient and accurate nonlinear programming method. Generation rescheduling and load shedding are the main controls used. The idea of adaptative local optimization is introduced, making the computation of appropriate generation rescheduling a very efficient process, Load shedding is used as a last resort, when further generation rescheduling is no longer possible. Heuristics are added in order to speed up the computation process and to take into account some practical aspects of power systems operation. A special procedure is carried out in case of critical situations, where emergency control actions are defined. The method's general idea is to keep the new secure operating point as close as possible to the original one while minimizing the amount of load shedding. The method can be a helpful tool for operation planning studies, security analysis, and reliability evaluation Of power systems. Simulations have been carried out for small test to large real life systems in order to show the effectiveness of the proposed method.
An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management under uncertainty. The interval and fuzzy robust programming methods were incorporated within...
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An interval-parameter fuzzy robust nonlinear programming (IFRNP) approach was developed for stream water quality management under uncertainty. The interval and fuzzy robust programming methods were incorporated within a general framework to address uncertainties associated with the nonlinear objective and the left- and right-hand sides of the constraints. A piecewise linearization approach was developed to deal with the nonlinear cost function. IFRNP could explicitly address complexities of various system uncertainties, where parameters were represented as both interval numbers and fuzzy membership functions. Furthermore, the dual uncertain information associated with the lower and upper bounds of each interval parameter could be effectively tackled through the concept of fuzzy boundary interval. The proposed IFRNP method was applied to a case of water quality management in the Guoyang section of the Guo River in Anhui province, China. A number of cost-effective schemes for water quality management were generated, and allowable wastewater discharge amounts were recommended. The results indicated that IFRNP was applicable to water quality management problems, where high nonlinearities and dual uncertainties exist.
We propose a trust region multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 15 (2005), pp. 17-38] is extended to solve constrained optimization prob...
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We propose a trust region multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 15 (2005), pp. 17-38] is extended to solve constrained optimization problems. The constraints are partitioned into p parts. The entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but also the individual behaviour of each part of the constraints is considered. The filter's entries and the acceptance criteria are different from other filter-related algorithms in the literature. It should be noted that the undesirable link between the objective function and the constraint violation function in the filter acceptance criteria disappears. Our algorithm is also combined with the non-monotone technique for accepting a trial step, which leads to a more flexible acceptance criteria. Under mild conditions, global convergence is proved. Numerical results show the robustness and efficiency of our algorithm.
The problem of packing ellipsoids is considered in the present work. Usually, the computational effort associated with numerical optimization methods devoted to packing ellipsoids grows quadratically with respect to t...
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The problem of packing ellipsoids is considered in the present work. Usually, the computational effort associated with numerical optimization methods devoted to packing ellipsoids grows quadratically with respect to the number of ellipsoids being packed. The reason is that the number of variables and constraints of ellipsoids' packing models is associated with the requirement that every pair of ellipsoids must not overlap. As a consequence, it is hard to solve the problem when the number of ellipsoids is large. In this paper, we present a nonlinear programming model for packing ellipsoids that contains a linear number of variables and constraints. The proposed model finds its basis in a transformation-based non-overlapping model recently introduced by Birgin et al. (J Glob Optim 65(4):709-743, 2016). For solving large-sized instances of ellipsoids' packing problems with up to 1000 ellipsoids, a multi-start strategy that combines clever initial random guesses with a state-of-the-art (local) nonlinear optimization solver is presented. Numerical experiments show the efficiency and effectiveness of the proposed model and methodology.
This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of or...
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This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualification is required. The optimality conditions are formulated in such a way that the gaps between the necessary and sufficient conditions are small and even vanish completely under mild constraint qualifications.
A framework for proving global convergence for a class of line search filter-type methods for nonlinear programming is presented without assuming that the Jacobian has full rank everywhere. The underlying method is ba...
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A framework for proving global convergence for a class of line search filter-type methods for nonlinear programming is presented without assuming that the Jacobian has full rank everywhere. The underlying method is based on the filter concept where trial points are accepted, provided there is a sufficient decrease in the objective function or constraints violation function. The proposed methods solve a sequence of quadratic programming subproblems via line search techniques to induce global convergence. Under mild conditions, we will also show that the algorithm converges two step superlinearly when the iterates are near to the solution.
Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for opt...
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Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for optima by updating generations. Particle swarm optimization has become the hotspot of evolutionary computation because of its excellent performance and simple implementation. After introducing the basic principle of the PSO, a particle swarm optimization algorithm embedded with constraint fitness priority-based ranking method is proposed in this paper to solve nonlinear programming problem. By designing the fitness function and constraints-handling method, the proposed PSO can evolve with a dynamic neighborhood and varied inertia weighted value to find the global optimum. The results from this preliminary investigation are quite promising and show that this algorithm is reliable and applicable to almost all of the problems in multiple-dimensional, nonlinear and complex constrained programming. It is proved to be efficient and robust by testing some example and benchmarks of the constrained nonlinear programming problems. (c) 2005 Elsevier Ltd. All rights reserved.
Generalized fuzzy c-means (GFCM) is an extension of fuzzy c-means using L-p-norm distances. However, existing methods cannot solve GFCM with m = 1. To solve this problem, we define a new kind of clustering models, cal...
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Generalized fuzzy c-means (GFCM) is an extension of fuzzy c-means using L-p-norm distances. However, existing methods cannot solve GFCM with m = 1. To solve this problem, we define a new kind of clustering models, called L p-norm probabilistic K-means (L-p-PKM). Theoretically, L p-PKM is equivalent to GFCM at m = 1, and can have nonlinear programming solutions based on an efficient active gradient projection (AGP) method, namely, inverse recursion maximum-step active gradient projection (IRMSAGP). On synthetic and UCI datasets, experimental results show that L p-PKM performs better than GFCM (m > 1) in terms of initialization robustness, p-influence, and clustering performance, and the proposed IRMSAGP also achieves better performance than the traditional AGP in terms of convergence speed.
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