162 research outputs found
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Full Newton Step Interior Point Method for Linear Complementarity Problem Over Symmetric Cones
In this thesis, we present a new Feasible Interior-Point Method (IPM) for Linear Complementarity Problem (LPC) over Symmetric Cones. The advantage of this method lies in that it uses full Newton-steps, thus, avoiding the calculation of the step size at each iteration. By suitable choice of parameters we prove the global convergence of iterates which always stay in the the central path neighborhood. A global convergence of the method is proved and an upper bound for the number of iterations necessary to find ε-approximate solution of the problem is presented
Numerical optimization for frictional contact problems
International audienc
Complexity analysis of primal-dual algorithms for the semidefinite linear complementarity problem
In this paper a primal-dual path-following interior-point algorithm for the monotone semidefinite linear complementarity problem is presented.
The algorithm is based on Nesterov-Todd search directions and on a suitable proximity for tracing approximately the central-path.
We provide an unified analysis for both long and small-update primal-dual algorithms.
Finally, the iteration bounds for these algorithms are obtained
- …