This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop em...
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This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.
In order to improve the control capability of the power system voltage stability and to enhance spatial and temporal coordination of voltage control means, it is essential to establish the model of emergency voltage c...
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The goal of this dissertation is to investigate the formulation and analysis of a trust-region interior-point method for solving nonconvex optimization problems with a mixture of equality and inequality constraints. T...
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The goal of this dissertation is to investigate the formulation and analysis of a trust-region interior-point method for solving nonconvex optimization problems with a mixture of equality and inequality constraints. The proposed method is based on minimizing a merit function that may be interpreted as a shifted primal-dual penalty-barrier function. The method generates a sequence of iterates with limit points that are either infeasible stationary points or complementary approximate Karush-Kuhn-Tucker points, i.e., every limit point satisfies reasonable stopping criteria and is a Karush-Kuhn-Tucker point under a regularity condition that is the weakest constraint qualification associated with sequential optimality conditions. Under suitable additional assumptions, the method is equivalent to a shifted variant of the primal-dual path-following method in the neighborhood of a solution. The proposed method has an inner/outer iteration structure. The outer iteration specifies the form of the merit function. The inner iteration optimizes the merit function with fixed parameters using a trust-region method. The algorithm for solving the trust-region subproblem involves a procedure based on the application of a one-dimensional Newton’s method. Methods are proposed for treating the so-called ”hard case” in which no root of the one dimensional equation exists.
In this paper, we consider a computational method of Stackelberg solutions for noncooperative two-level nonlinear programming problems (TLNLPPs) which contain two decision makers with different priorities. For the pur...
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Regression analysis fits predictive models to data on a response variable and corresponding values for a set of explanatory variables. Often data on the explanatory variables come at a cost from commercial databases, ...
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Regression analysis fits predictive models to data on a response variable and corresponding values for a set of explanatory variables. Often data on the explanatory variables come at a cost from commercial databases, so the available budget may limit which ones are used in the final model. In this dissertation, two budget-constrained regression models are proposed for continuous and categorical variables respectively using Mixed Integer nonlinear programming (MINLP) to choose the explanatory variables to be included in solutions. First, we propose a budget-constrained linear regression model for continuous response variables. Properties such as solvability and global optimality of the proposed MINLP are established, and a data transformation is shown to signicantly reduce needed big-Ms. Illustrative computational results on realistic retail store data sets indicate that the proposed MINLP outperforms the statistical software outputs in optimizing the objective function under a limit on the number of explanatory variables selected. Also our proposed MINLP is shown to be capable of selecting the optimal combination of explanatory variables under a budget limit covering cost of acquiring data sets. A budget-constrained and or count-constrained logistic regression MINLP model is also proposed for categorical response variables limited to two possible discrete values. Alternative transformations to reduce needed big-Ms are included to speed up the solving process. Computational results on realistic data sets indicate that the proposed optimization model is able to select the best choice for an exact number of explanatory variables in a modest amount of time, and these results frequently outperform standard heuristic methods in terms of minimizing the negative log-likelihood function. Results also show that the method can compute the best choice of explanatory variables affordable within a given budget. Further study adjusting the objective function to minimize the Bayesi
The Car Sequencing Problem is a NP-hard problem which has been used extensively in the literature as a benchmark for testing different formulations. Most of these approaches are based on Heuristics and Constraint Logi...
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ISBN:
(纸本)9781622763528
The Car Sequencing Problem is a NP-hard problem which has been used extensively in the literature as a benchmark for testing different formulations. Most of these approaches are based on Heuristics and Constraint Logic programming. This paper proposes a Non Linear programming methodology to solve a particular case of the Car Sequencing Problem in which the main constraints are the capacity of the Wide and Paint Body Storages.
A hybrid method, which combines the pure primal- dual interior point algorithm (PDIPA) and the predictor- corrector primal-dual interior point algorithm (PCPDIPA) for optimal power flows presented in [1], is proposed....
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