Using the so-called aggregate function of the constraints, a new aggregate constraint homotopy (ACH) is constructed and corresponding interior path following method for smooth programming is proposed. It was proved th...
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Using the so-called aggregate function of the constraints, a new aggregate constraint homotopy (ACH) is constructed and corresponding interior path following method for smooth programming is proposed. It was proved that under a weak normal cone condition, the ACH determines a smooth interior path from a given interior point to a K-K-T point. This forms the theoretical base of ACH method.
We present a general filter algorithm that allows a great deal of freedom in the step computation. Each iteration of the algorithm consists basically in computing a point which is not forbidden by the filter, from the...
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We present a general filter algorithm that allows a great deal of freedom in the step computation. Each iteration of the algorithm consists basically in computing a point which is not forbidden by the filter, from the current point. We prove its global convergence, assuming that the step must be efficient, in the sense that, near a feasible nonstationary point, the reduction of the objective function is "large." We show that this condition is reasonable, by presenting two classical ways of performing the step which satisfy it. In the first one, the step is obtained by the inexact restoration method of Martinez and Pilotta. In the second, the step is computed by sequential quadratic programming.
Magnetometer is a significant sensor for integrated navigation. However, it suffers from many kinds of unknown dynamic magnetic disturbances. We study the problem of online estimating such disturbances via a nonlinear...
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Magnetometer is a significant sensor for integrated navigation. However, it suffers from many kinds of unknown dynamic magnetic disturbances. We study the problem of online estimating such disturbances via a nonlinear optimization aided by the intermediate quaternion estimation from inertial fusion. The proposed optimization is constrained by the geographical distribution of the magnetic field forming a constrained nonlinear programming. The uniqueness of the solution has been verified mathematically, and we design an interior-point-based solver for efficient computation on embedded chips. It is claimed that the designed scheme mainly outperforms in dealing with the challenging bias estimation problem under static motion as the previous representatives can hardly achieve. Experimental results demonstrate the effectiveness of the proposed scheme on high accuracy, fast response, and low computational load.
A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive a...
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A dynamic optimization model for weed infestation control using selective herbicide application in a corn crop system is presented. The seed bank density of the weed population and frequency of dominant or recessive alleles are taken as state variables of the growing cycle. The control variable is taken as the dose-response function. The goal is to reduce herbicide usage, maximize profit in a pre-determined period of time and minimize the environmental impacts caused by excessive use of herbicides. The dynamic optimization model takes into account the decreased herbicide efficacy over time due to weed resistance evolution caused by selective pressure. The dynamic optimization problem involves discrete variables modeled as a nonlinear programming (NLP) problem which was solved by an active set algorithm (ASA) for box-constrained optimization. Numerical simulations for a case study illustrate the management of the Bidens subalternans in a corn crop by selecting a sequence of only one type of herbicide. The results on optimal control discussed here will give support to make decision on the herbicide usage in regions where weed resistance was reported by field observations.
This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable fu...
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This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuously differentiable functions. The importance of tilt stability has been well recognized from both theoretical and numerical perspectives of optimization, and this area of research has drawn much attention in the literature, especially in recent years. Based on advanced techniques of variational analysis and generalized differentiation, we derive here complete pointbased second-order characterizations of tilt-stable minimizers entirely in terms of the initial program data under the new qualification conditions, which are the weakest ones for the study of tilt stability.
In this paper, we study recourse-based stochastic nonlinear programs and make two sets of contributions. The first set assumes general probability spaces and provides a deeper understanding of feasibility and recourse...
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In this paper, we study recourse-based stochastic nonlinear programs and make two sets of contributions. The first set assumes general probability spaces and provides a deeper understanding of feasibility and recourse in stochastic nonlinear programs. A sufficient condition, for equality between the sets of feasible first-stage decisions arising from two different interpretations of almost sure feasibility, is provided. This condition is an extension to nonlinear settings of the "W-condition," first suggested by Walkup and Wets (SIAM J. Appl. Math. 15:1299-1314, 1967). Notions of complete and relatively-complete recourse for nonlinear stochastic programs are defined and simple sufficient conditions for these to hold are given. Implications of these results on the L-shaped method are discussed. Our second set of contributions lies in the construction of a scalable, superlinearly convergent method for solving this class of problems, under the setting of a finite sample-space. We present a novel hybrid algorithm that combines sequential quadratic programming (SQP) and Benders decomposition. In this framework, the resulting quadratic programming approximations while arbitrarily large, are observed to be two-period stochastic quadratic programs (QPs) and are solved through two variants of Benders decomposition. The first is based on an inexact-cut L-shaped method for stochastic quadratic programming while the second is a quadratic extension to a trust-region method suggested by Linderoth and Wright (Comput. Optim. Appl. 24:207-250, 2003). Obtaining Lagrange multiplier estimates in this framework poses a unique challenge and are shown to be cheaply obtainable through the solution of a single low-dimensional QP. Globalization of the method is achieved through a parallelizable linesearch procedure. Finally, the efficiency and scalability of the algorithm are demonstrated on a set of stochastic nonlinear programming test problems.
A test problem generator, by means of neural networks nonlinear function approximation capability, is given in this paper which provides test problems, with many predetermined local minima and a global minimum, to eva...
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A test problem generator, by means of neural networks nonlinear function approximation capability, is given in this paper which provides test problems, with many predetermined local minima and a global minimum, to evaluate nonlinear programming algorithms that are designed to solve the problem globally.
The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dyn...
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The most effective numerical techniques for the solution of trajectory optimization and optimal control problems combine a nonlinear iteration procedure with some type of parametric approximation to the trajectory dynamics. Early methods attempted to parameterize the dynamics using a small number of variables because the iterative search procedures could not successfully solve larger problems. With the development of more robust nonlinear programming algorithms, it is now feasible and desirable to consider formulations of the trajectory optimization problem incorporating a large number of variables and constraints. The purpose of this paper is to address the manner in which a trajectory is parameterized and the design of the nonlinear programming algorithm to effectively deal with this formulation.
We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and pos...
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We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.
Optimization of an ammonia-water absorption refrigeration system, minimizing operating and annualized capital costs, is described. A mixed-integer nonlinear programming (MINLP) model, with the inclusion of discontinuo...
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Optimization of an ammonia-water absorption refrigeration system, minimizing operating and annualized capital costs, is described. A mixed-integer nonlinear programming (MINLP) model, with the inclusion of discontinuous functions for capital costs for the main components of the system, is presented. The minimum total annualized cost is achieved with the simultaneous optimization of seven design variables. Practical limits of the design variables are established for the purpose of generating design parameters in accordance with the type of system studied. The model is applied to two examples. The analysis considers two types of heat rejection media: cooling water and air. The results obtained indicate that the selection of cooling medium is dependent on the refrigeration level that is required. The optimum configuration and operating conditions do not correspond to the best process integration and the coefficients of performance, and irreversibilities are high. The design variables with the highest impact on the objective function are dependent on the heat rejection medium characteristics and the process requirements. A sensitivity analysis of the effects of the evaluation criteria on the minimization of operating and capital costs is presented.
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