Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(?) of the form min x f(x, ?), s.t.x εR(?). Such properties off* and the solution set...
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Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(?) of the form min x f(x, ?), s.t.x εR(?). Such properties off* and the solution set mapS* form an important part of the theoretical basis for sensitivity, stability, and parametric analysis in mathematical optimization. Sufficient conditions are given for several standard types of convexity and concavity off*, in terms of respective convexity and concavity assumptions onf and the feasible region point-to-set mapR. Specializations of these results to the general parametric inequality-equality constrained nonlinear programming problem and its right-hand-side version are provided. To the authors' knowledge, this is the most comprehensive compendium of such results to date. Many new results are given.
This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properti...
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This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10000 samples are used as a reference solution for evaluation of the accuracy of the proposed method.
In this paper, a new algorithm for solving constrained nonlinear programming problems is presented. The basis of our proposed algorithm is none other than the necessary and sufficient conditions that one deals within ...
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In this paper, a new algorithm for solving constrained nonlinear programming problems is presented. The basis of our proposed algorithm is none other than the necessary and sufficient conditions that one deals within a discrete constrained local optimum in the context of the discrete Lagrange multipliers theory. We adopt a revised particle swarm optimization algorithm and extend it toward solving nonlinear programming problems with continuous decision variables. To measure the merits of our algorithm, we provide numerical experiments for several renowned benchmark problems and compare the outcome against the best results reported in the literature. The empirical assessments demonstrate that our algorithm is efficient and robust. (C) 2010 Elsevier Ltd. All rights reserved.
An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations gi...
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An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is more difficult to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed several different approaches. However, when we try to follow these approaches in an interactive animation system where the object on which to operate is as highly articulated as a realistic human figure, they fail in either generality or performance. So, we approach this problem through nonlinear programming techniques. It has been successfully used since 1988 in the spatial constraint system within Jack(R), a human figure simulation system developed at the University of Pennsylvania, and proves to be satisfactorily efficient, controllable, and robust. A spatial constraint in our system involves two parts: one constraint on the figure, the end-effector, and one on the spatial environment, the goat. These two parts are dealt with separately, so that we can achieve a neat modular implementation. Constraints can be added one at a time with appropriate weights designating the importance of this constraint relative to the others and are always solved as a group. If physical limits prevent satisfaction of all the constraints, the system stops with the (possibly local) optimal solution for the given weights. Also, the rigidity of each joint angle can be controlled, which is useful for redundant degrees of freedom.
This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle ...
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This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle swarm optimization to solve augmented Lagrangian penalty function. In doing so, the algorithm launches into a global search over the solution space while keeping a detailed exploration into the neighborhoods. To shed light on the merit of the algorithm, we provide a test bed consisting of 30 test problems to compare our algorithm against two of its variations along with two state-of-the-art nonlinear optimization algorithms. The numerical experiments illustrate that the proposed algorithm makes an effective use of hybrid framework when dealing with nonlinear equality constraints although its convergence cannot be guaranteed. (C) 2012 Elsevier Ltd. All rights reserved.
Quality function deployment (QFD) is a methodology to ensure that customer requirements (CRs) are deployed through product planning, part development, process planning and production planning. The first step to implem...
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Quality function deployment (QFD) is a methodology to ensure that customer requirements (CRs) are deployed through product planning, part development, process planning and production planning. The first step to implement QFD is to identify CRs and assess their relative importance weights. This paper proposes a nonlinear programming (NLP) approach to assessing the relative importance weights of CRs, which allows customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats. The proposed NLP approach does not require any transformation of preference formats and thus can avoid information loss or information distortion. Its potential applications in assessing the relative importance weights of CRs in QFD are illustrated with a numerical example.
In this paper, the development and application of a new upper bound limit method for two- and three-dimensional (2D and 3D) slope stability problems is presented. Rigid finite elements are used to construct a kinemati...
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In this paper, the development and application of a new upper bound limit method for two- and three-dimensional (2D and 3D) slope stability problems is presented. Rigid finite elements are used to construct a kinematically admissible velocity field. Kinematically admissible velocity discontinuities are permitted to occur at all inter-element boundaries. The proposed method formulates the slope stability problem as an optimization problem based on the upper bound theorem. The objective function for determination of the minimum value of the factor of safety has a number of unknowns that are subject to a set of linear and nonlinear equality constraints as well as linear inequality constraints. The objective function and constrain equations are derived from an energy-work balance equation, the Mohr-Coulomb failure (yield) criterion, an associated flow rule, and a number of boundary conditions. The objective function with constraints leads to a standard nonlinear programming problem, which can be solved by a sequential quadratic algorithm. A computer program has been developed for finding the factor of safety of a slope, which makes the present method simple to implement. Four typical 2D and 3D slope stability problems are selected from the literature and are analysed using the present method. The results of the present limit analysis are compared with those produced by other approaches reported in the literature.
A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not...
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A second-order dual to a nonlinear programming problem is formulated. This dual uses the Fritz John necessary optimality conditions instead of the Karush-Kuhn-Tucker necessary optimality conditions, and thus, does not require a constraint qualification. Weak, strong, strict-converse, and converse duality theorems between primal and dual problems are established. (C) 2001 Elsevier Science Ltd. All rights reserved.
We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively dec...
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We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd-Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato's effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. (C) 2012 Elsevier Ltd. All rights reserved.
The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired ei...
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The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil. (C) 2015 Elsevier Ltd. All rights reserved.
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