System identification of a dynamical model of a vehicle using data generated by a high-fidelity simulator

Unmanned vehicles are a vital topic in today’s science and technology field. The safety problem of unmanned vehicles has been paid more attention from researchers. People are continually developing new control technologies, making the auxiliary driving or control of vehicles more accurate and reliable. Before designing a reliable controller,...

Combined shape and size optimization of an offshore crane

Tetrahedron is working on a new design for large offshore cranes that can lift higher. This is necessary due to the increasing size of offshore wind turbines, and the inability of the conventional cranes to scale up without needing a larger ship that is carrying them. To compute the forces working on the trusses of the crane structure,...

Mathematical formulations and algorithms for fast and robust power system simulations

During the normal operation, control and planning of the power system, grid operators employ numerous tools including the Power Flow (PF) and the Optimal Power Flow (OPF) computations to keep the balance in the power system. The solution of the PF computation is used to assess whether the power system can function properly for the given...

Optimization of stiffened panels using a combination of FEM and a predictor-corrector interior point method

Structural optimization, first introduced by Schmidt in 1960, is a rapid growing factor in the development of new aerospace structures. This growth is established by the increase in numerical modelling techniques, cheaper computer power, the increasing cost of production and competition between companies. The combination of both structural...

Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

In this paper, we design a class of infeasible interior-point methods for linear optimization based on large neighborhood. The algorithm is inspired by a full-Newton step infeasible algorithm with a linear convergence rate in problem dimension that was recently proposed by the second author. Unfortunately, despite its good numerical behavior,...

An Improved and Simplified Full-Newton Step O(n) Infeasible Interior-Point Method for Linear Optimization

We present an improved version of an infeasible interior-point method for linear optimization published in 2006. In the earlier version each iteration consisted of one so-called feasibility step and a few---at most three---centering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the...

A Variational Formulation for Thin Membranes

Membrane structures have a rich history of use across many disciplines and are widely used in aerospace and structural engineering applications. A few examples can be found in solar sails, atmospheric balloons and parachutes. These membranes have many advantages, including their ability to take complex shapes and their low mass to surface ratio,...

Large-Update Infeasible Interior-Point Methods for Linear Optimization

Recently, C. Roos proposed a full-Newton step infeasible interior-point method (IIPM) for linear optimization (LO). Shortly afterwards, Mansouri and Roos presented a variant of this algorithm and Gu et al. a version with a simplified analysis. Roos' algorithm is a path-following method. It uses the so-called homotopy path as a guideline to an...

Kernel-based interior-point methods for monotone linear complementarity problems over symmetric cones

We present an interior-point method for monotone linear complementarity problems over symmetric cones (SCLCP) that is based on barrier functions which are defined by a large class of univariate functions, called eligible kernel functions. This class is fairly general and includes the classical logarithmic function, the self-regular functions, as...

Unified Analysis of Kernel-Based Interior-Point Methods for P?(?)-Linear Complementarity Problems

We present an interior-point method for the P?(?)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non...

Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization

We present several improvements of the full-Newton step infeasible interior-point method for linear optimization introduced by Roos (SIAM J. Optim. 16(4):1110–1136, 2006). Each main step of the method consists of a feasibility step and several centering steps. We use a more natural feasibility step, which targets the ?+-center of the next pair...

Full-step interior-point methods for symmetric optimization

In [SIAM J. Optim., 16(4):1110--1136 (electronic), 2006] Roos proposed a full-Newton step Infeasible Interior-Point Method (IIPM) for Linear Optimization (LO). It is a primal-dual homotopy method; it differs from the classical IIPMs in that it uses only full steps. This means that no line searches are needed. In this thesis, we first present an...

Kernel-function based algorithms for semidefinitie optimization

Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interiorpoint methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper...

A new full-Newton step O(n) infeasible interior-point algorithm for semidefinite optimization

Interior-point methods for semidefinite optimization have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, the second author designed a primal-dual infeasible interior-point algorithm with the currently best iteration bound for linear optimization problems. Since the algorithm uses only full Newton...

A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization

In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the classical logarithmic function, the prototype self-regular function, and non-self-regular kernel functions as special cases. The analysis of the...

Jordan algebraic approach to symmetric optimization

In this thesis we present a generalization of interior-point methods for linear optimization based on kernel functions to symmetric optimization. It covers the three standard cases of conic optimization: linear optimization, second-order cone optimization and semi-definite optimization. We give an introduction to Euclidean Jordan algebras and...

Interior Point Methods for Semidefinite Programming