2020. February 13.

**MEGHÍVÓ**

**Szeretettel meghívjuk Rigó Petra Renáta PhD értekezés házi védésére**

**2020. február 19-én csütörtökön 16 órára**

**Helyszín: BME H. épület 405/a terem**

Absztrakt:

__New trends in algebraic equivalent transformation of the central path and its applications __

The aim of this thesis is to propose, develop and analyse new interior-point algorithms. We also investigate the possibility of extending some interior-point algorithms from linear optimization to more general problems, such as linear complementarity problems and symmetric optimization problems. The leading thread through this presentation is the algebraic equivalent transformation technique in the context of interior-point algorithms. This method plays an important role in the theory of interior-point algorithms, because using it we can define new search directions that yield new algorithms.

One of the novelties of this thesis is that we apply a new function, namely the difference of the identity map and the square root function on the centering equation of the system defining the central path. The barrier associated to this function cannot be derived from a usual kernel function. Therefore, we introduce a new notion, namely the concept of the positive-asymptotic kernel function. We also present the relationship of the algebraic equivalent transformation technique to other approaches to determine search directions. Furthermore, we present four interior-point algorithms for solving different types of optimization problems that use the difference of the identity map and the square root function in the algebraic equivalent transformation technique. We present the complexity analysis of the proposed algorithms and we show that the methods retain the best known polynomial iteration complexity.