A nonlinear programming Excel Workbook (Microsoft Corporation, Redmond, WA) was developed using the Excel Solver (Frontline Systems Inc., Incline Village, NV) to optimize energy density and bird performance. In this s...
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A nonlinear programming Excel Workbook (Microsoft Corporation, Redmond, WA) was developed using the Excel Solver (Frontline Systems Inc., Incline Village, NV) to optimize energy density and bird performance. In this study, 6 dietary treatments (2.535, 2.635, 2.735, 2.835, 2.935, and 3.035 Mcal of ME/kg) were fed to Hy-Line W-36 laying hens (n = 192) in phase 2 (from 32 to 44 wk of age). Data were fitted to quadratic equations to express egg mass, feed consumption, and the objective function return over feed cost in terms of energy density. To demonstrate the capabilities of the model, the prices for eggs, corn, and soybean meal were increased and decreased by 25% and the program was solved for the maximum profit and optimized feed mix. By increasing the egg price, the model changed the optimal diet formulation and energy density in such a way as to improve performance and feed consumption, and accepted a higher energy concentration. Therefore, egg producers can realize considerable savings from using the nonlinear programming model described here, as opposed to a linear programming model with fixed minima for energy and other nutrients. These savings result from the ability of the nonlinear programming models to determine the most profitable energy density that should be fed as energy and protein prices change.
Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin pro...
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Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin problem. This transformation is done by using a generalized Lagrange multiplier technique. Such an approach permits us to use Newton's and gradient methods for nonlinear programming. Convergence proofs are provided, and some numerical results are given.
This paper concerns large-scale general (nonconvex) nonlinear programming when first and second derivatives of the objective and constraint functions are available. A method is proposed that is based on finding an app...
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This paper concerns large-scale general (nonconvex) nonlinear programming when first and second derivatives of the objective and constraint functions are available. A method is proposed that is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved with a modified Newton method that generates search directions from a primal-dual system similar to that proposed for interior methods. The augmented penalty-barrier function may be interpreted as a merit function for values of the primal and dual variables. An inertia-controlling symmetric indefinite factorization is used to provide descent directions and directions of negative curvature for the augmented penalty-barrier merit function. A method suitable for large problems can be obtained by providing a version of this factorization that will treat large sparse indefinite systems.
nonlinear programming is a complex methodology where a problem is mathematically expressed in terms of optimality while imposing constraints on feasibility. Such problems are formulated by humans and solved by optimiz...
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nonlinear programming is a complex methodology where a problem is mathematically expressed in terms of optimality while imposing constraints on feasibility. Such problems are formulated by humans and solved by optimization algorithms. We support domain experts in their challenging tasks of understanding and troubleshooting optimization runs of intricate and high-dimensional nonlinear programs through a visual analytics system. The system was designed for our collaborators' robot motion planning problems, but is domain agnostic in most parts of the visualizations. It allows for an exploration of the iterative solving process of a nonlinear program through several linked views of the computational process. We give insights into this design study, demonstrate our system for selected real-world cases, and discuss the extension of visualization and visual analytics methods for nonlinear programming.
This paper describes an accelerated multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems. The unconstrained problems are solved...
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This paper describes an accelerated multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems. The unconstrained problems are solved using a rank-one recursive algorithm described in an earlier paper. Multiplier estimates are obtained by minimizing the error in the Kuhn-Tucker conditions using a quadratic programming algorithm. The convergence of the sequence of unconstrained problems is accelerated by using a Newton-Raphson extrapolation process. The numerical effectiveness of the algorithm is demonstrated on a relatively large set of test problems.
This paper is concerned with a pair of naturally symmetric problems related by duality. Self-duality has been investigated for the class of non-differentiable convex programs.
This paper is concerned with a pair of naturally symmetric problems related by duality. Self-duality has been investigated for the class of non-differentiable convex programs.
We introduce a family of new transforms based on imitating the proximal mapping of Moreau and the associated Moreau-Yosida proximal approximation of a function. The transforms are constructed in terms of the phi-diver...
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We introduce a family of new transforms based on imitating the proximal mapping of Moreau and the associated Moreau-Yosida proximal approximation of a function. The transforms are constructed in terms of the phi-divergence functional (a generalization of the relative entropy) and of Bregman's measure of distance. An analogue of Moreau's theorem associated with these entropy-like distances is proved. We show that the resulting Entropic Proximal Maps share properties similar to the proximal mapping and provide a fairly general framework for constructing approximation and smoothing schemes for optimization problems. Applications of the results to the construction of generalized augmented Lagrangians for nonlinear programs and the minimax problem are presented.
The purpose of this paper is to study various duality results in nonlinear programming for pseudo-invex functions. Such results were known in the literature for invex functions.
The purpose of this paper is to study various duality results in nonlinear programming for pseudo-invex functions. Such results were known in the literature for invex functions.
Environmental protection, shortage of fresh-water and rising costs for wastewater treatment are all convincing motives for reducing fresh-water consumption and wastewater discharge of the chemical, petrochemical, petr...
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Environmental protection, shortage of fresh-water and rising costs for wastewater treatment are all convincing motives for reducing fresh-water consumption and wastewater discharge of the chemical, petrochemical, petroleum refining and other process industries. Maximizing water reuse, regeneration re-use, and regeneration recycling within the chemical plant, as well as optimal distribution of waste streams for end-of-pipe treatment can reduce fresh-water usage and wastewater discharge, while they are also significant in shrinking capital investment in wastewater treatment systems. Optimal assignment and design of water consuming, regenerating, and treatment systems is a complicated task that can be mathematically formulated as mixed integer non-linear programming (MINLP). In the present article the superstructure based 'Cover and Eliminate' approach with NLP is applied with the tools of the GAMS/MINOS/CONOPT package and compared to previous results. After introducing the problem in the context of chemical process synthesis, a mathematical model is described and the use of the methodology is explained. Experience with the use of GAMS is discussed. Several case studies are solved including basic examples from the literature and their variants. The main conclusion is that the application of the mathematical programming for the optimal water allocation problem is essential owing to the broad variety of the specification opportunities. The complex nature of re-use, regeneration re-use, and recycling with multiple pollutants and multiple treatment processes cannot be simultaneously taken into account by conceptual approaches. It is also shown that the assumption on the independency of contamination rates, generally applied in earlier works, are nor necessarily valid;and the NLP approach can deal with the more reliable specifications.
The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve th...
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The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.
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