We present a filter line search method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety but uses a robust (always feasible) subproblem based on an exact penalty fu...
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We present a filter line search method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety but uses a robust (always feasible) subproblem based on an exact penalty function to compute a search direction. This contrasts traditional filter methods that use a (separate) restoration phase designed to reduce infeasibility until a feasible subproblem is obtained. Therefore, an advantage of our approach is that every trial step is computed from subproblems that value reducing both the constraint violation and the objective function. Moreover, our step computation involves subproblems that are computationally tractable and utilize second derivative information when it is available. The formulation of each subproblem and the choice of weighting parameter is crucial for obtaining an efficient, robust, and practical method. Our strategy is based on steering methods designed for exact penalty functions but is fortified with a trial step convexification scheme that ensures that a single quadratic optimization problem is solved per iteration. Moreover, we use local feasibility estimates that emerge during the steering process to define a new and improved margin (envelope) of the filter. Under common assumptions, we show that the iterates converge to a local first-order solution of the optimization problem from an arbitrary starting point.
In this paper, a bio-inspired computational intelligence technique is presented for solving nonlinear doubly singular system using artificial neural networks (ANNs), genetic algorithms (GAs), sequentialquadratic prog...
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In this paper, a bio-inspired computational intelligence technique is presented for solving nonlinear doubly singular system using artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and their hybrid GA-SQP. The power of ANN models is utilized to develop a fitness function for a doubly singular nonlinear system based on approximation theory in the mean square sense. Global search for the parameters of networks is performed with the competency of GAs and later on fine-tuning is conducted through efficient local search by SQP algorithm. The design methodology is evaluated on number of variants for two point doubly singular systems. Comparative studies with standard results validate the correctness of proposed schemes. The consistent correctness of the proposed technique is proven through statistics using different performance indices.
Abstract-This article describes a multi-objective optimization method to solve the optimal distributed generation sizing and placement. The optimization problem considers two objectives: minimizing the total real powe...
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Abstract-This article describes a multi-objective optimization method to solve the optimal distributed generation sizing and placement. The optimization problem considers two objectives: minimizing the total real power losses of the network and minimizing the overall distributed generation installation cost. The objectives are combined into a scalar objective optimization problem by using weighted sum method. Both objective functions and equality and inequality constraints are formulated as a non-linear program and solved by a sequential quadratic programming deterministic technique. The multi-objective optimization method gives several answers instead of a single (unique) one. These answers are optimal, and the designer (decision maker) can select the proper solution according to subjective preferences. These optimum results are known as the Pareto front. A fuzzy decision-making procedure for order preference is used for finding the best compromise solution from the set of Pareto solutions. The proposed method is tested using a 15-bus radial distribution system to show its applicability. A comparative study is performed to evaluate two cases-a single distributed generation unit installation and a multiple distributed generation installation-ending by a comparative study of the two cases.
A novel design potential method that integrates the probabilistic constraint evaluation closely into the design optimization process Is presented for robust system parameter design. From a broader perspective, it is s...
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A novel design potential method that integrates the probabilistic constraint evaluation closely into the design optimization process Is presented for robust system parameter design. From a broader perspective, it is shown that the probabilistic constraints can be evaluated using either the conventional reliability index approach or the proposed performance measure approach. The performance measure approach is inherently robust and is more effective when the probabilistic constraint is inactive. The reliability index approach is more effective for the violated probabilistic constraint, but it could yield singularity when the probabilistic constraint is inactive. Moreover, the close coupling of performance probability analysis and design optimization is illustrated in a proposed unified system space, The design potential method, which is developed to take full advantage of the important design information obtained from the previous probabilistic constraint evaluation, can significantly accelerate the convergence of the reliability-based design optimization process.
We propose a method for constrained and unconstrained nonlinear multiobjective optimization problems that is based on an SQP-type approach. The proposed algorithm maintains a list of nondominated points that is improv...
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We propose a method for constrained and unconstrained nonlinear multiobjective optimization problems that is based on an SQP-type approach. The proposed algorithm maintains a list of nondominated points that is improved both for spread along the Pareto front and optimality by solving single-objective constrained optimization problems. These single-objective problems are derived as SQP problems based on the given nondominated points. Under appropriate differentiability assumptions we discuss convergence to local optimal Pareto points. We provide numerical results for a set of unconstrained and constrained multiobjective optimization problems in the form of performance and data profiles, where several performance metrics are used. The numerical results confirm the superiority of the proposed algorithm against a state-of-the-art multiobjective solver and a classical scalarization approach, both in the quality of the approximated Pareto front and in the computational effort necessary to compute the approximation.
We consider solving mathematical programs with complementarity constraints (MPCCs) as nonlinear programs (NLPs) using standard NLP solvers. This approach is appealing because it allows existing off-the-shelf NLP solve...
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We consider solving mathematical programs with complementarity constraints (MPCCs) as nonlinear programs (NLPs) using standard NLP solvers. This approach is appealing because it allows existing off-the-shelf NLP solvers to tackle large instances of MPCCs. Numerical experience on MacMPEC, a large collection of MPCC test problems is presented. Our experience indicates that sequential quadratic programming (SQP) methods are very well suited for solving MPCCs and at present outperform interior-point solvers both in terms of speed and reliability. All NLP solvers also compare very favorably to special MPCC solvers on tests published in the literature.
We consider optimal design of physical systems described by a nonlinear boundary value problem. We propose a sequential quadratic programming method specifically tailored to the solution of this class of design proble...
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We consider optimal design of physical systems described by a nonlinear boundary value problem. We propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems. A particular representation of the null space of the constraint Jacobian that exploits its specific structure is employed. The resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches. Three variants of the method are developed and discussed. These entail the solution of either two or three linear systems involving the Jacobian matrix of the discretized form of the boundary value problem. The method is used to solve aerodynamic design problems involving nonlinear transonic flow. No special provisions are made for treating discontinuities, and therefore the present implementation of the method is limited to problems with no shocks. Problems with up to 90 shape design variables are solved. Numerical results demonstrate a substantial performance improvement over conventional methods.
The REQP algorithm solves constrained minimization problems using a sequential quadratic programming technique based on the properties of penalty functions. The convergence of REQP has been studied elsewhere (Refs. 1,...
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The REQP algorithm solves constrained minimization problems using a sequential quadratic programming technique based on the properties of penalty functions. The convergence of REQP has been studied elsewhere (Refs. 1, 2). This paper uses a novel approach to the analysis of the method near to the solution, based on the use of conjugate subspaces. The step p taken by a constrained minimization algorithm can be thought of as having two components, h in the subspace tangential to the constraints and upsilon in the subspace spanned by the constraint normals. It is usual for h and upsilon to be orthogonal components. Recently, Dixon (Ref. 3) has suggested constructing p from components which are not orthogonal. That is, we write p = h' + upsilon', where h' is in the subspace tangential to the constraints and where upsilon' and h' are conjugate with respect to the Hessian of the Lagrangian function. By looking at the conjugate components of the REQP search directions, it is possible to simplify the analysis of the behavior near the solution and to obtain new results about the local rate of convergence of the method.
Gould and Robinson [SIAM J. Optim., 20 (2010), pp. 2023-2048] proved global convergence of a second derivative SQP method for minimizing the exact l(1)-merit function for a fixed value of the penalty parameter. This r...
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Gould and Robinson [SIAM J. Optim., 20 (2010), pp. 2023-2048] proved global convergence of a second derivative SQP method for minimizing the exact l(1)-merit function for a fixed value of the penalty parameter. This result required the properties of a so-called Cauchy step, which was itself computed from a so-called predictor step. In addition, they allowed for the additional computation of a variety of (optional) accelerator steps that were intended to improve the efficiency of the algorithm. The main purpose of this paper is to prove that a nonmonotone variant of the algorithm is quadratically convergent for two specific realizations of the accelerator step;this is verified with preliminary numerical results on the Hock and Schittkowski test set. Once fast local convergence is established, we consider two specific aspects of the algorithm that are important for an efficient implementation. First, we discuss a strategy for defining the positive-definite matrix B(k) used in computing the predictor step that is based on a limited-memory BFGS update. Second, we provide a simple strategy for updating the penalty parameter based on approximately minimizing the l(1)-penalty function over a sequence of increasing values of the penalty parameter.
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