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Design optimization for symmetrical gravity retaining walls
Erol Sadoğlu, 2014, original scientific article

Abstract: The optimization for symmetrical gravity retaining walls of different heights is examined in this study. For this purpose, an optimization problem of continuous functions is developed. The continuous functions are the objective function defined as the cross-sectional area of the wall and the constraint functions derived from external stability and internal stability verifications. The verifications are listed as the overturning, the forward sliding, the bearing capacity, the shears in the stem and the bendings in the stem. The heights of the walls are selected as 2.0, 3.0, and 4.0 m in order to investigate the outline of the optimum cross-section and the effect of the wall height on the outline. Additionally, the physical and mechanical properties of the soil are kept constant in order to compare only the effect of the height on the geometry. The upper and lower bounds of the solution space are specified to be as wide as possible and the minimum dimensions suggested for the gravity retaining walls are not taken into account. A common feature of the optimum cross-sections of walls with different heights is to have a very wide lower part like a wall foundation and a slender stem. However, other than the forward sliding constraint, the bending constraints are active at the optimum values of the variables.
Keywords: gravity retaining wall, nonlinear optimization, continuous variables, interior point method
Published in DKUM: 14.06.2018; Views: 1289; Downloads: 160
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Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimization
Pakize Taylan, Gerhard-Wilhelm Weber, 2008, original scientific article

Abstract: A central element in organization of financal means by a person, a company or societal group consists in the constitution, analysis and optimization of portfolios. This requests the time-depending modeling of processes. Likewise many processes in nature, technology and economy, financial processes suffer from stochastic fluctuations. Therefore, we consider stochastic differential equations (Kloeden, Platen and Schurz, 1994) since in reality, especially, in the financial sector, many processes are affected with noise. As a drawback, these equations are hard to represent by a computer and hard to resolve. In our paper, we express them in simplified manner of approximation by both a discretization and additive models based on splines. Our parameter estimation refers to the linearly involved spline coefficients as prepared in (Taylan and Weber, 2007) and the partially nonlinearly involved probabilistic parameters. We construct a penalized residual sum of square for this model and face occuring nonlinearities by Gauss-Newton's and Levenberg-Marquardt's method on determining the iteration step. We also investigate when the related minimization program can be written as a Tikhonov regularization problem (sometimes called ridge regression), and we treat it using continuous optimization techniques. In particular, we prepare access to the elegant framework of conic quadratic programming. These convex optimation problems are very well-structured, herewith resembling linear programs and, hence, permitting the use of interior point methods (Nesterov and Nemirovskii, 1993).
Keywords: stochastic differential equations, regression, statistical learning, parameter estimation, splines, Gauss-Newton method, Levenberg-Marquardt's method, smoothing, stability, penalty methods, Tikhonov regularization, continuous optimization, conic quadratic programming
Published in DKUM: 10.01.2018; Views: 1237; Downloads: 137
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