We propose and analyze an inexact version of the modifiedsubgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate,...
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We propose and analyze an inexact version of the modifiedsubgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may allow to solve problems with less computational effort. We illustrate this through test problems, including an optimal bang-bang control problem, under several different inexactness schemes.
A new approach to compute optimal forcing functions for nonlinear dynamic systems expressed by differential equations and stemming from the sliding mode control (SMC) problems is presented. SMC input achieves generati...
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A new approach to compute optimal forcing functions for nonlinear dynamic systems expressed by differential equations and stemming from the sliding mode control (SMC) problems is presented. SMC input achieves generation of a desired trajectory in two phases. In the first phase, the input is designed to steer the state of the nonlinear dynamic system towards a stable (hyper) surface (in practice, it is generally a subspace) in the state space. The second phase starts once the state enters a prespecified neighbourhood of the surface. In this phase, the control input is required to drive the system state towards the origin while keeping it in this neighbourhood. It is shown that by appropriate selection of the objective functions and the constraints, it is possible to model both phases of this problem in the form of constrained optimization problems, which provide an optimal solution direction and thus improve the chattering. Generally, these problems are not convex and therefore require a special solution approach. The modifiedsubgradient algorithm, which serves for solving a large class of nonconvex optimization problems, is used here for solving the optimization problems so constructed. This article also proposes a generalized optimization problem with a unified objective function by taking a weighted sum of two objectives representing the two stages. Validity of the approach of this work is illustrated by stabilizing a two-link planar robot manipulator.
This paper gives a general model for the faculty course assignment problem that is a zero-one nonlinear multiobjective programming problem. Because of the nonconvexity of the problem, simple weighting scalarization do...
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This paper gives a general model for the faculty course assignment problem that is a zero-one nonlinear multiobjective programming problem. Because of the nonconvexity of the problem, simple weighting scalarization does not guarantee finding all Pareto-optimal solutions. Therefore, a newly developed three step process consisting of the Analytic Hierarchy Process, scalarization and the subgradientmethod is provided to deal with the problem. This approach is used to solve a nonconvex multiobjective faculty course assignment problem for the first time. A real life application is included. (C) 2003 Elsevier B.V. All rights reserved.
This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated w...
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This paper presents the recently introduced modified subgradient method for optimization and its effectiveness in a fuzzy transportation model. Here a multi-item balanced transportation problem (MIBTP) is formulated where unit transportation costs are imprecise. Also available spaces and budgets at destinations are limited but imprecise. The objective is to find a shipment schedule for the items that minimizes the total cost subjected to imprecise warehouse and budget constraints at destinations. The proposed model is reduced to a multi-objective optimization problem using tolerances, then to a crisp single-objective one using fuzzy non-linear programming (FNLP) technique and Zimmermann's method. The above fuzzy MIBTP is also reduced to another form of deterministic one using modified sub-gradient method (MSM). These two crisp optimization problems are solved by Genetic Algorithm (GA). As an extension, fuzzy multi-item balanced solid transportation problems (STPs) with and without restrictions on some routes and items are formulated and reduced to deterministic ones following FNLP and Zimmermann's methods. These models are also solved by GA. Models are illustrated numerically, optimum results of fuzzy MIBTP from two deductions are compared. Results are also presented for different GA parameters. Crown Copyright (C) 2013 Published by Elsevier B. V. All rights reserved.
We treat the sliding mode control problem by formulating it as a two phase problem consisting of reaching and sliding phases. We show that such a problem can be formulated as bicriteria nonlinear programming problem b...
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We treat the sliding mode control problem by formulating it as a two phase problem consisting of reaching and sliding phases. We show that such a problem can be formulated as bicriteria nonlinear programming problem by associating each of these phases with an appropriate objective function and constraints. We then scalarize this problem by taking weighted sum of these objective functions. We show that by solving a sequence of such formulated nonlinear programming problems it is possible to obtain sliding mode controller feedback coefficients which yield a competitive performance throughout the control. We solve the nonlinear programming problems so constructed by using the modified subgradient method which does not require any convexity and differentiability assumptions. We illustrate validity of our approach by gencrating a sliding mode control input function for stabilization of an inverted pendulum. (c) 2005 Elsevier Inc. All rights reserved.
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