In this paper, a formulation of an interior-point Newton method for general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic ra...
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In this paper, a formulation of an interior-point Newton method for general nonlinear programming problems is presented. The formulation uses the Coleman-Li scaling matrix. The local convergence and the q-quadratic rate of convergence for the method are established under the standard assumptions of the Newton method for general nonlinear programming.
In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice c...
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In 1988 Kennedy and Chua introduced the dynamical canonical nonlinear programming circuit (NPC) to solve in real time nonlinear programming problems where the objective function and the constraints are smooth (twice continuously differentiable) functions. In this paper, a generalized circuit is introduced (G-NPC), which is aimed at solving in real time a much wider class of nonsmooth nonlinear programming problems where the objective function and the constraints are assumed to satisfy only the weak condition of being regular functions. G-NPC, which derives from a natural extension of NPC, has a neural-like architecture and also features the presence of constraint neurons modeled by ideal diodes with infinite slope in the conducting region. By using the Clarke's generalized gradient of the involved functions, G-NPC is shown to obey a gradient system of differential inclusions, and its dynamical behavior and optimization capabilities, both for convex and nonconvex problems, are rigorously analyzed in the frame-' work of nonsmooth analysis and the theory of differential inclusions. In. the special important cas ' e of linear and quadratic programming problems, salient dynamical features of G-NPC, namely the presence of sliding modes, trajectory convergence infinite time, and the ability to compute the exact optimal solution of the problem being modeled, are uncovered and explained in the developed analytical framework.
The paper considers an example of Wachter and Biegler which is shown to converge to a nonstationary point for the standard primal-dual interior-point method for nonlinear programming. The reason for this failure is an...
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The paper considers an example of Wachter and Biegler which is shown to converge to a nonstationary point for the standard primal-dual interior-point method for nonlinear programming. The reason for this failure is analyzed and a heuristic resolution is discussed. The paper then characterizes the performance of LOQO, a line-search interior-point code, on a large test set of nonlinear programming problems. Specific types of problems which can cause LOQO to fail are identified.
This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that improves either the objective f...
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This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that improves either the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, penalty constants, or Lagrange multipliers. A key feature of the new algorithm is that it preserves the division into search and local poll steps, which allows the explicit use of inexpensive surrogates or random search heuristics in the search step. It is shown here that the algorithm identifies limit points at which optimality conditions depend on local smoothness of the functions and, to a greater extent, on the choice of a certain set of directions. Stronger optimality conditions are guaranteed for smoother functions and, in the constrained case, for a fortunate choice of the directions on which the algorithm depends. These directional conditions generalize those given previously for linear constraints, but they do not require a feasible starting point. In the absence of general constraints, the proposed algorithm and its convergence analysis generalize previous work on unconstrained, bound constrained, and linearly constrained generalized pattern search. The algorithm is illustrated on some test examples and on an industrial wing planform engineering design application.
In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired feature...
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In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired features: exactness and smoothness if the constraints and objective function are differentiable. All exact penalty result is proved for the objective penalty function. In addition to these results, based on the objective penalty function, we develop an algorithm for solving the original problem and show its convergence under some mild conditions. (C) 2004 Elsevier Ltd. All rights reserved.
This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-depende...
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This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.
Many practical problems often lead to large nonconvex nonlinear programming problems that have many equality constraints. The global optimization algorithms of these problems have received much attention over the last...
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Many practical problems often lead to large nonconvex nonlinear programming problems that have many equality constraints. The global optimization algorithms of these problems have received much attention over the last few years. Generally, stochastic algorithms are suitable for these problems, but not efficient when there are too many equality constraints. Therefore, a global optimization algorithm for solving these problems is proposed in this paper. The new algorithm, based on a feasible set strategy, uses a stochastic algorithm and a deterministic local algorithm. The convergence of the algorithm is analyzed. This algorithm is applied to practical problem, and the numerical results illustrate the accuracy and efficiency of the algorithm. (C) 2003 Elsevier Inc. All rights reserved.
In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a feasibility phase, which reduces a measure of infeasibility,...
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In this paper we present a filter algorithm for nonlinear programming and prove its global convergence to stationary points. Each iteration is composed of a feasibility phase, which reduces a measure of infeasibility, and an optimality phase, which reduces the objective function in a tangential approximation of the feasible set. These two phases are totally independent, and the only coupling between them is provided by the filter. The method is independent of the internal algorithms used in each iteration, as long as these algorithms satisfy reasonable assumptions on their efficiency. Under standard hypotheses, we show two results: for a filter with minimum size, the algorithm generates a stationary accumulation point;for a slightly larger filter, all accumulation points are stationary.
In this article, we consider a lower order penalty function and its epsilon-smoothing for an inequality constrained nonlinear programming problem. It is shown that any strict local minimum satisfying the second-order ...
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In this article, we consider a lower order penalty function and its epsilon-smoothing for an inequality constrained nonlinear programming problem. It is shown that any strict local minimum satisfying the second-order sufficiency condition for the original problem is a strict local minimum of the lower order penalty function with any positive penalty parameter. By using an epsilon-smoothing approximation to the lower order penalty function, we get a modified smooth global exact penalty function under mild assumptions.
A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit ma...
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A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.
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