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On a modified subgradient algorithm for dual problems via sharp augmented Lagrangian
 Journal of Global Optimization
, 2006
"... We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condit ..."
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We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the stepsize parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. Key words: Nonconvex programming; nonsmooth optimization; augmented Lagrangian; sharp Lagrangian; subgradient optimization.
c ○ TÜB˙ITAK Solving Fuzzy Linear Programming Problems with Linear Membership Functions
"... In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the righthand side and the technological coefficients are fuzzy numbers. We consider here only the ca ..."
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In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the righthand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are nonlinear and even nonconvex in general. We propose here the “modified subgradient method ” and use it for solving these problems. We also compare the new proposed method with well known “fuzzy decisive set method”. Finally, we give illustrative examples and their numerical solutions. Key Words: Fuzzy linear programming; fuzzy number; modified subgradient method; fuzzy decisive set method.
Stabilizing Acrobot by Using Nonlinear Programming Based on Sliding Mode Controller
"... Proceedings, pp. 712—724 We design sliding mode controllers for nonlinear dynamic systems by using a nonlinear programming approach. We show that by appropriate selection of the objective function and the constraints, it is possible to obtain sliding mode controller parameters by solving a sequence ..."
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Proceedings, pp. 712—724 We design sliding mode controllers for nonlinear dynamic systems by using a nonlinear programming approach. We show that by appropriate selection of the objective function and the constraints, it is possible to obtain sliding mode controller parameters by solving a sequence of nonlinear programming problems. These parameters determine the forcing function which satisfies possibly nonlinear, even nonconvex constraints and optimize a given nonlinear objective function. We use the Modified Subgradient Algorithm for the nonconvex optimization problems encountered in computing such forcing functions. We illustrate the validity of our approach by stabilizing an underactuated two link robot manipulator, called Acrobot, at vertically upright position.