In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust nonlinear programming [Zhang, Y.: J. Optim. Theory Appl. 132, 111-124 (2007)]. Three robust...
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In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust nonlinear programming [Zhang, Y.: J. Optim. Theory Appl. 132, 111-124 (2007)]. Three robust nonlinear programming problems were chosen from the literature using the criteria that results calculated using other methods must be available and the problems should be realistic, but fairly simple. Our studies show that the first-order method produced reasonable solutions when the level of uncertainty was small to moderate. In addition, we demonstrate a method for leveraging a theoretical result to eliminate constraint violations. Since the first-order method is relatively inexpensive in comparison to other robust optimization techniques, our studies indicate that, under moderate uncertainty, the first-order approach may be more suitable than other methods for large problems.
This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search di...
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This paper proposes a line search filter reduced Hessian method for nonlinear equality constrained optimization. The feature of the presented algorithm is that the reduced Hessian method is used to produce a search direction, a backtracking line search procedure to generate step size, some filtered rules to determine step acceptance, second order correction technique to reduce infeasibility and overcome the Maratos effects. It is shown that this algorithm does not suffer from the Maratos effects by using second order correction step, and under mild assumptions fast convergence to second order sufficient local solutions is achieved. The numerical experiment is reported to show the effectiveness of the proposed algorithm. (C) 2011 Elsevier Inc. All rights reserved.
Automatic assignment of tolerances to dimensioned mechanical assemblies is studied as an optimization problem;the objective of which is to minimize the (manufacturing) cost, subject to the constraints of (design) func...
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Automatic assignment of tolerances to dimensioned mechanical assemblies is studied as an optimization problem;the objective of which is to minimize the (manufacturing) cost, subject to the constraints of (design) functionality and (assembly) interchangeability. By associating a nominal dimension and a tolerance to the variance, a probabilistic approach is adopted. Trigonometric functions relating the component geometries give rise to the nonlinearity in the system. Estimating an n-dimensional nonlinear integral by a polytope converts the probabilistic optimization formulation to a deterministic one. It also allows rapid evaluation of tolerance analysis embedded in tolerance synthesis. Local optimality is ensured by analysis of convexity and quasi-concavity of the objective function and some of the constraints. Sensitivity analysis is performed to provide search directions for global optimality. An implementation is reported with an example.
We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial ...
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We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the solution of the corresponding initial value problem converges to the set of critical points, (c) every strict local minimum is locally asymptotically stable, (d) the feasible set is a positively invariant set, and (e) the dynamical system is given explicitly and does not involve the unknown critical points of the problem. No convexity assumption is employed. The construction of the family of dynamical systems is based on an extension of the control Lyapunov function methodology, which employs extensions of LaSalle's theorem and are of independent interest. Examples illustrate the obtained results.
The past few years have led to the development of a novel large-scale nonlinear programming solver called IPOPT. Described in Wachter and Biegler (2004), this algorithm uses a barrier formulation for inequality constr...
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The past few years have led to the development of a novel large-scale nonlinear programming solver called IPOPT. Described in Wachter and Biegler (2004), this algorithm uses a barrier formulation for inequality constraints and incorporates a new filter line search algorithm. It also includes a number of features that make it efficient and robust even for highly nonlinear problems. In particular, it is well suited to exploit second derivatives. The code has been used on thousands on test problems ranging in size up to almost two million variables. Finally, enhancements of this method have been made to deal with complementarity conditions that model a class of discrete decisions with continuous variables. This paper describes the development of CAPE-OPEN compliant objects for IPOPT to solve dynamic optimization problems. This activity complements a number of tasks to develop interfaces to optimization modelling platforms such as AIMMS and AMPL. Here we consider protocols such as Equation Set Objects (ESO) and the MINLP CAPE-OPEN interface to IPOPT (CO-LaN Consortium, 2002). The resulting object can be linked to other objects that are CAPE-OPEN compliant. We also describe a preprocessing procedure for generic models that leads to efficient optimization problem formulations for IPOPT. To validate the interface and the preprocessing procedure, we present a comprehensive optimization case study that links to dynamic optimization models written in gPROMS. In addition, future plans for the development, enhancement and distribution of IPOPT will be outlined.
In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker station...
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In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems. (C) 2009 Elsevier B.V. All rights reserved.
This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of p...
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This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear La- grange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associ- ated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems.
This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear/fractional transformation (LFT). We formulate an output-error identification pr...
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This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear/fractional transformation (LFT). We formulate an output-error identification problem and present a parameter estimation scheme in which a prediction error-based cost function is minimized using nonlinear programming;its gradients and (approximate) Hessians can be completed using LPV fillers and inner products, and identifiable model sets (i.e., local canonical forms) are obtained efficiently using a natural geometrical approach. Some computational issues and experiences are discussed, and a simple numerical example is provided for illustration.
The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qu...
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The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qualification. The first order necessary conditions are of Karush-Kuhn-Tucker type.
Riveted joints are expected to satisfy the requirements of strength, tightness, stiffness and in some cases heat and electric conductivity. Furthermore, the production time and cost should be minimal. Conventional des...
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Riveted joints are expected to satisfy the requirements of strength, tightness, stiffness and in some cases heat and electric conductivity. Furthermore, the production time and cost should be minimal. Conventional design procedures are effectively iterative techniques whose length and results are mainly dependent on designer intuition and experience. The design procedure in many cases is terminated when a feasible, however rarely the best, solution is reached. In this paper, an optimization procedure which eliminates the trial and error approach, is developed. This procedure determines the riveted joint configuration that minimizes production costs while satisfying stress and dimensional constraints. The calculation method which is based on non-linear programming techniques, is successfully applied to the rivited joints of two braking systems.
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