作者：
Nie, Pu-YanJinan Univ
Dept Math Guangzhou 510632 Peoples R China Hunan Univ
Coll Econ & Trade Changsha 410079 Peoples R China
Penalty function methods, presented many years ago, play exceedingly important roles in the optimization community. According to numerical results, penalty function approaches work very efficiently for equality constr...
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Penalty function methods, presented many years ago, play exceedingly important roles in the optimization community. According to numerical results, penalty function approaches work very efficiently for equality constrained problems. For inequality constrained problems, sequential quadratic programming (SQP) approaches do better than that of sequential penalty quadratical programming (SlQP) methods. Taking these into account, we propose another optimization approach, in which we aim to combine the advantages of penalty function techniques and SQP approaches. In the new technique, equality constraints are handled by penalty function technique, while inequality constraints are still treated as constraints. The corresponding theories are exploited in this work. The theories of the corresponding augmented Lagrangian function, especially quadratic augmented penalty methods, are also achieved. A new kind of penalty method, combining the advantages of SQP and SlQP, is therefore developed in this work. (c) 2006 Elsevier Ltd. All rights reserved.
This paper proposes a new necessary condition for the infeasibility of nonlinear optimization problems, that becomes also sufficient under a convexity assumption, which is stated as a Pareto-criticality condition of a...
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This paper proposes a new necessary condition for the infeasibility of nonlinear optimization problems, that becomes also sufficient under a convexity assumption, which is stated as a Pareto-criticality condition of an auxiliary multi-objective optimization problem. This condition is evaluated in a search that either leads to a feasible point or to a point at which the infeasibility conditions hold. The resulting infeasibility certificate has global validity in convex problems and has at least a local meaning in generic nonlinear problems. (C) 2016 Elsevier B.V. All rights reserved.
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.
A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained throug...
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A two-step topology-finding method based on mixed integer programming and nonlinear programming is proposed for tensegrity structures. In the first step, feasible and symmetric strut connectivities are obtained through a ground structure method combined with mixed integer programming;in the second step, the cable connectivities are optimized through nonlinear programming to obtain a feasible tensegrity structure. The same ground structure used in the first step is adopted in the second step, which is beneficial to find a more symmetric cable layout. The independent continuous mapping method is used in the second step to convert the 0-1 binary variables of cable connectivities to continuous variables to transform the combinatorial optimization problem into a nonlinear programming problem. The number of strut lengths is adopted as a control parameter and a symmetry objective function is proposed to generate a variety of regular and symmetric tensegrity structures. A multi-stage computation scheme is proposed to improve the computational efficiency. Typical examples are carried out to validate the proposed method. The computational efficiency of the method is benchmarked with existing methods fully based on mixed integer programming. Results demonstrate that the computational efficiency of the proposed method is significantly improved compared to the existing methods.
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.
Based on the introduction of some new concepts of semifeasible direction, Feasible Degree (FD1) of semifeasible direction, feasible degree (FD2) of illegal points 'belonging to' feasible domain, etc., this pap...
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Based on the introduction of some new concepts of semifeasible direction, Feasible Degree (FD1) of semifeasible direction, feasible degree (FD2) of illegal points 'belonging to' feasible domain, etc., this paper proposed a new fuzzy method for formulating and evaluating illegal points and three new kinds of evaluation functions and developed a special Hybrid Genetic Algorithm (HGA) with penalty function and gradient direction search for nonlinear programming problems. It uses mutation along the weighted gradient direction as its main operator and uses arithmetic combinatorial crossover only in the later generation process. Simulation of some examples show that this method is effective. (C) 1998 Elsevier Science Ltd. All rights reserved.
A computerized mathematical procedure based on nonlinear programming is presented for the purpose of a sandy soil parameter prediction problem by inverse analysis. The task of inverse analysis is to evaluate the value...
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A computerized mathematical procedure based on nonlinear programming is presented for the purpose of a sandy soil parameter prediction problem by inverse analysis. The task of inverse analysis is to evaluate the values of input parameters for a specified output or response of the system. This inverse problem to determine the values of system input parameters is mathematically formulated as a constrained optimization problem in this study. The input parameters are considered as design variables. The constraint set is developed through the implementation of lower and upper bound on design variables. The objective function is determined by evaluating the error or mismatch between the specified output (reference value) and the model predicted value for a given design vector. The resulting nonlinear programming problem is solved using the Interior Penalty Function method coupled with the Davidon-Fletcher-Powell method and quadratic interpolation scheme. To demonstrate the proposed methodology, two illustrative examples related to axially loaded piles installed in sandy soil medium are considered. The numerical results indicate that the back analyzed values are in good agreement with their respective reference values.
We present an approach for nonlinear programming based on the direct minimization of an exact differentiable penalty function using trust-region Newton techniques. The approach provides desirable features required for...
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We present an approach for nonlinear programming based on the direct minimization of an exact differentiable penalty function using trust-region Newton techniques. The approach provides desirable features required for scalability: it can detect and exploit directions of negative curvature, it is superlinearly convergent, and it enables the scalable computation of the Newton step through iterative linear algebra. Moreover, it presents features that are desirable for parametric optimization problems that must be solved in a latency-limited environment, as is the case for model predictive control and mixed-integer nonlinear programming. These features are fast detection of activity, efficient warm starting, and progress on a primal-dual merit function at every iteration. We note that other algorithmic approaches fail to satisfy at least one of these features. We derive general convergence results for our approach and demonstrate its behavior through numerical studies.
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.
Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable...
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Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable solution is obtained. We avoid this by formulating and solving the mesh design problem as a mathematical program. Our approach simultaneously modifies both mesh size (h) and local polynomial order (p) to yield an "optimal" mesh for a target error or given computational cost with gradients from local convergence rates. Constraints such as the one irregularity rule during mesh refinement are systematically incorporated in this formulation. The design task leads to a mixed integer nonlinear program (MINLP), that is relaxed to an NLP. To reduce the computations for the NLP, we employ simplified analytical gradients derived from initial mesh calculations. Finally, we apply our method to three model problems showing that complex hp-adaptive grids can be obtained directly from a uniform coarse grid. A commercial optimization software, MINOS [B.A. Murtagh, M.A. Saunders, MINOS 5.4 User's Guide, Technical Report SOL 83-20R, Stanford University, Stanford, 1987, Revised February 1995], was used as the NLP optimizer. (C) 2001 Elsevier Science B.V. All rights reserved.
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