相关论文: On quadratic optimization problems and canonical d…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
The distributed optimal synchronization problem with linear quadratic cost is solved in this paper for multi-agent systems with an undirected communication topology. For the first time, the optimal synchronization problem is formulated as a…
Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…
This report aims to present the main ideas of Regge calculus necessary to understand the basic premise of CDT. Next, the main strategy of the CDT approach is introduced in general terms. The main focus of this report is the 2-D model of…
Solving optimization tasks using variational quantum algorithms has emerged as a crucial application of the current noisy intermediate-scale quantum devices. However, these algorithms face several difficulties like finding suitable ansatz…
We study the optimization version of the equal cardinality set partition problem (where the absolute difference between the equal sized partitions' sums are minimized). While this problem is NP-hard and requires exponential complexity to…
Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…
Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially…
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
We study a job shop scheduling problem for an automatized robot in a high-throughput laboratory and a travelling salesperson problem with recently proposed digitized counterdiabatic quantum optimization (DCQO)algorithms. In DCQO, we find…
In this paper it is shown that the compact linearization approach, that has been previously proposed only for binary quadratic problems with assignment constraints, can be generalized to arbitrary linear equations with positive coefficients…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
Recently there has been a surge of interest in optimal decision tree (ODT) methods that globally optimize accuracy directly, in contrast to traditional approaches that locally optimize an impurity or information metric. However, the value…
In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
We present an algorithm to compute all $n$ nondominated points of a multicriteria discrete optimization problem with $d$ objectives using at most $\mathcal{O}(n^{\lfloor d/2 \rfloor})$ scalarizations. The method is similar to algorithms by…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…