Study of optimization algorithms for lightweight structures

Topology optimization (TO) is a relatively new numerical optimization technique for designing optimal engineering structures. The main purpose of this thesis is the review of constrained optimizers such as the Bisection and the Augmented Lagrangian scheme and the development and implementation of two constrained optimizers including the incorporation of fmincon, an optimizer of the Matlab’s optimization toolbox, and a Null Space optimizer. All of them will be used in combination of the unconstrained optimizers SLERP (for Level-Set function) and Projected Gradient (for density variables). Different optimization problems of different complexity will be evaluated using one objective function with the aim of the determine and validate the efficiency of the optimizers. Thus, the runtime and the local minimum reached will be evaluated. Finally, the best solutions achieved will be 3D printed

A Sequential Quadratic Programming Method for Optimization with Stochastic Objective Functions, Deterministic Inequality Constraints and Robust Subproblems

In this paper, a robust sequential quadratic programming method of [1] for constrained optimization is generalized to problem with stochastic objective function, deterministic equality and inequality constraints. A stochastic line search scheme in [2] is employed to globalize the steps. We show that in the case where the algorithm fails to terminate in finite number of iterations, the sequence of iterates will converge almost surely to a Karush-Kuhn-Tucker point under the assumption of extended Mangasarian-Fromowitz constraint qualification. We also show that, with a specific sampling method, the probability of the penalty parameter approaching infinity is 0. Encouraging numerical results are reported

Estimation of coefficients for modelling ships from sea trials using stepwise optimization methods and considering trim and draught conditions

This thesis proposes a method for estimation of the hydrodynamic coefficients using full-scale sea trials and the system identification. Also, based on this, a proposal for a new estimation method that can consider various trim and draught conditions is given here. The new estimation method is in the form of suggesting an additional correction formula that can complement the existing empirical estimation formulas for the hydrodynamic coefficients involving different trim and draught parameters

Numerical Methods for PDE Constrained Optimization with Uncertain Data

Optimization problems governed by partial differential equations (PDEs) arise in many applications in the form of optimal control, optimal design, or parameter identification problems. In most applications, parameters in the governing PDEs are not deterministic, but rather have to be modeled as random variables or, more generally, as random fields. It is crucial to capture and quantify the uncertainty in such problems rather than to simply replace the uncertain coefficients with their mean values. However, treating the uncertainty adequately and in a computationally tractable manner poses many mathematical challenges. The numerical solution of optimization problems governed by stochastic PDEs builds on mathematical subareas, which so far have been largely investigated in separate communities: Stochastic Programming, Numerical Solution of Stochastic PDEs, and PDE Constrained Optimization. The workshop achieved an impulse towards cross-fertilization of those disciplines which also was the subject of several scientific discussions. It is to be expected that future exchange of ideas between these areas will give rise to new insights and powerful new numerical methods

An elastic primal active-set method for structured QPs

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Moving Horizon Estimation for the Two-tank System

This thesis presents the application and evaluation of Moving Horizon Estimation (MHE) for the nonlinear two-tank system. MHE is an iterative optimization-based approach that continuously updates the estimates of the states by solving an optimization problem over a fixed-size, receding horizon. Linear and nonlinear MHE-based estimators are designed and implemented in Matlab for evaluation in simulation environment and Simulink for on-line realization and validation. The linear and nonlinear MHE are evaluated in comparison with the Kalman and Extended Kalman filter through extensive simulations and experimental validation, assessing their accuracy, efficiency, and overall performance. The results of the two-tank state and unmeasured disturbance estimation shows the benefit of the MHE

Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization problems with DC constraints and prove its convergence. Then we combine the proposed algorithm with a relaxation technique to handle inconsistent linearizations. Numerical tests are performed to investigate the behaviour of the class of algorithms.Comment: 18 pages, 1 figur