Related papers: Finding two-dimensional peaks
Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much…
In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum…
The global optimization have the very extensive applications in econometrics, science and engineering. However, the global optimization for non-convex objective functions is particularly difficult since most of the existing global…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspects: (i) the proposed particle filter is a controlled…
We propose a swarm-based optimization algorithm inspired by air currents of a tornado. Two main air currents - spiral and updraft - are mimicked. Spiral motion is designed for exploration of new search areas and updraft movements is…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
Quantum annealing is a new method for finding extrema of multidimensional functions. Based on an extension of classical, simulated annealing, this approach appears robust with respect to avoiding local minima. Further, unlike some of its…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally…
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm…
The particle swarm optimization (PSO) algorithm has been recently introduced in the non--linear programming, becoming widely studied and used in a variety of applications. Starting from its original formulation, many variants for…
A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the…
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic…
Swarm intelligence is all about developing collective behaviours to solve complex, ill-structured and large-scale problems. Efficiency in collective behaviours depends on how to harmonise the individual contributions so that a complementary…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…