In this paper, we provide local convergence analysis for the two phase nonlinear Polyhedral Active Set Algorithm (NPASA) designed to solve nonlinear programs. In particular, we establish local quadratic convergence of...
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In this paper, we discuss an exact augumented Lagrangian functions for the nonlinear programming problem with both equality and inequality constraints, which is the generation of the augmented Lagrangian function in c...
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ISBN:
(纸本)9783037851579
In this paper, we discuss an exact augumented Lagrangian functions for the nonlinear programming problem with both equality and inequality constraints, which is the generation of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relationship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipliers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.
In this paper we consider a distributed optimization problem, where a set of agents interacting and cooperating locally have as common goal the minimization of a function expressed as a sum of (possibly non-convex) di...
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ISBN:
(纸本)9781479978878
In this paper we consider a distributed optimization problem, where a set of agents interacting and cooperating locally have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum is associated with an agent and each agent has assigned an inequality constraint, therefore generating an optimization problem with inequality constraints. In this paper we present a distributed algorithm for solving such a problem, and give local convergence results. Our approach is based on solving (in a centralized manner) an equivalent augmented optimization problem with mixed constraints. The structure of this augmented problem ensures that the resulting algorithm is distributed. The main challenge in proving the convergence results comes from the fact that the local minimizers are no longer regular due to the distributed formulation. We present also an extension of this algorithm that solves a constrained optimization problem, where each agent has both equality and inequality constraints.
Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm wh...
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Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm which distributes the work of numerical optimization to several simultaneously computing processors. The method is applied to different structural engineering design problems that demonstrate this usefulness, satisfaction or potential. The computing algorithm has been given and discussed for a designer who can program it without difficulty.
The problem of locating p maximally dispersed points in a convex space is considered. This problem is formulated as a non-linear programming problem. It is shown that this problem, in a square, is equivalent to the pr...
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The problem of locating p maximally dispersed points in a convex space is considered. This problem is formulated as a non-linear programming problem. It is shown that this problem, in a square, is equivalent to the problem of packing the square with p equal circles of largest possible radius. Computational experience with the non-linear programming formulation of the dispersion problem is reported. Four of the solutions found are superior to the best known solutions in the literature for the corresponding circle-packing problem.
In their seminal paper, Hammer, Rosemberg, and Rudeanu present an algebraic approach, the Basic Algorithm (BA), for solving the Unconstrained Binary nonlinear programming Problem (UBNLP). BA sequentially eliminates va...
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This paper presents an efficient and reliable partitioning Gradient Based (PGB) algorithm for solving nonlinear Goal programming (NLGP) Problems. The PGB algorithm uses the partitioning technique developed for linear ...
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This paper presents an efficient and reliable partitioning Gradient Based (PGB) algorithm for solving nonlinear Goal programming (NLGP) Problems. The PGB algorithm uses the partitioning technique developed for linear GP problems, to decompose the NLGP problem into a series of single objective nonlinear problems. It begins by considering only those constraints associated with the first priority, and uses the Generalized Reduced Gradient (GRG) method to solve the first subproblem. If a unique optimal solution is reached, the algorithm terminates with the current point as the optimal solution to the entire NLGP;otherwise, the second subproblem is solved by adding the second priority goal constraints and a linear constraint to retain the first priority and minimizing the second priority objective. This procedure is continued until all the subproblems are solved or unique optimal solution is detected at any subproblem. A sufficient test is developed to detect unique solutions for nonlinear problems. The PGB algorithm is tested against the Modified Pattern Search (MPS) method, currently available for solving NLGP problems. The results indicate that the PGB algorithm always outperforms the MPS method except for some small problems. In addition, the PGB method found the optimal solution for all test Problems proving its robustness and reliability, while the MPS method failed in more than half of the test problems by converging to a nonoptimal point.
It is well known that the availability of cost-effective and powerful parallel computers has enhanced the ability of the operations research community to solve laborious computational problems. But many researchers ar...
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It is well known that the availability of cost-effective and powerful parallel computers has enhanced the ability of the operations research community to solve laborious computational problems. But many researchers argue that the lack of portability of parallel algorithms is a major drawback to utilizing parallel computers. This paper studies the performance of a portable parallel unconstrained non-gradient optimization algorithm, when executed in various shared-memory multiprocessor systems, compared with its non-portable code. Analysis of covariance is used to analyse how the algorithm's performance is affected by several factors of interest. The results yield more insights into the parallel computing.
To find nonlinear minimization problems are considered and standard C2-regularity assumptions on the criterion function and constrained functions are reduced to C1,1-regularity. With the aid of the generalized second ...
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To find nonlinear minimization problems are considered and standard C2-regularity assumptions on the criterion function and constrained functions are reduced to C1,1-regularity. With the aid of the generalized second order directional derivative for C1,1 real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.
作者：
Montiel Lopez, P.Ruiz Galan, M.Univ Granada
Dept Sci Ctr Estudios Superiores Inmaculada C Toaguina Eguaras 144 Granada 18018 Spain Univ Granada
Dept Appl Math ETS Ingn Edificac C Severo Ochoa S-N E-18071 Granada Spain
The aim of this paper is to state a sharp version of the Konig supremum theorem, an equivalent reformulation of the Hahn-Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker...
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The aim of this paper is to state a sharp version of the Konig supremum theorem, an equivalent reformulation of the Hahn-Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker and Fritz John types, for nonlinear infinite programs. We also show that a weak concept of convexity coming from minimax theory, infsup-convexity, is the adequate one for this kind of results. (C) 2017 Elsevier Inc. All rights reserved.
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