arXiv subjects

Tamas Terlaky

Publications and source records attributed to Tamas Terlaky.

4 recordsLinked to original sources

arXiv2021

On computing the nonlinearity interval in parametric semidefinite optimization

This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the notions of invariancy set, nonlinearity interval, and transition point of the optimal partition, and we investigate their characterizations. We show that the set of transition points is finite and the continuity of the optimal set mapping, on the basis of Painlevé-Kuratowski set convergence, might fail on a nonlinearity interval. Under a local nonsingularity condition, we then develop a methodology, stemming from numerical algebraic geometry, to efficiently compute nonlinearity intervals and transition points of the optimal partition. Finally, we support the theoretical results by applying our procedure to some numerical examples.

math.OC↗

arXiv2021

On the sensitivity of the optimal partition for parametric second-order conic optimization

In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called invariancy set and nonlinearity interval, which serve as stability regions of the optimal partition. We then propose, under the strict complementarity condition, an iterative procedure to compute a nonlinearity interval of the optimal partition. Furthermore, under primal and dual nondegeneracy conditions, we show that a boundary point of a nonlinearity interval can be numerically identified from a nonlinear reformulation of the parametric second-order conic optimization problem. Our theoretical results are supported by numerical experiments.

math.OC↗

arXiv2021

Quantum Circuit Design Search

This article explores search strategies for the design of parameterized quantum circuits. We propose several optimization approaches including random search plus survival of the fittest, reinforcement learning both with classical and hybrid quantum classical controllers and Bayesian optimization as decision makers to design a quantum circuit in an automated way for a specific task such as multi-labeled classification over a dataset. We introduce nontrivial circuit architectures that are arduous to be hand-designed and efficient in terms of trainability. In addition, we introduce reuploading of initial data into quantum circuits as an option to find more general designs. We numerically show that some of the suggested architectures for the Iris dataset accomplish better results compared to the established parameterized quantum circuit designs in the literature. In addition, we investigate the trainability of these structures on the unseen dataset Glass. We report meaningful advantages over the benchmarks for the classification of the Glass dataset which supports the fact that the suggested designs are inherently more trainable.

quant-ph↗

arXiv2019

Parametric analysis of semidefinite optimization

In this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behavior of the optimal partition and optimal set mapping on a so-called nonlinearity interval. Furthermore, we investigate the sensitivity of the approximation of the optimal partition in a nonlinearity interval, which has been recently studied by Mohammad-Nezhad and Terlaky. The approximation of the optimal partition was obtained from a bounded sequence of interior solutions on, or in a neighborhood of the central path. We derive an upper bound on the distance between the approximations of the optimal partitions of the original and perturbed problems. Finally, we examine the theoretical bounds by way of experimentation.

math.OC↗