Numerical solving the Schrödinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose two high-...

Serverless computing is one of the latest technologies that has received much attention from researchers and companies in recent years since it provides dynamic scalability and a clear economic model. Serverless computing enables users to pay only ...

We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions, i.e., $F(\mathit{...}\mathit{}\mathit{}$

Leveraging inexpensive and human intervention-based annotating methodologies, such as crowdsourcing and web crawling, often leads to datasets with noisy labels. Noisy labels can have a detrimental impact on the performance and generalization of ...

We study divide-and-conquer recurrences of the form f ( n ) = α f ( ⌊ n 2 ⌋ ) + β f ( ⌈ n 2 ⌉ ) + g ( n ) ( n ⩾ 2 ) , with g ( n ) and f ( 1 ) given, where α , β ⩾ 0 with α + β > 0; such recurrences appear often in the analysis of computer ...

We present a new type of location-based queries, namely the Budget Range-based All Neighboring Object Group Query (BR-ANOGQ for short), to offer spatial object information while respecting distance and budget range constraints. This query type ...${}^{\mathit{}}$${}_{}{}_{}$

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet ...

• A classification on Nash equilibrium algorithms in the literature with basic ideas on design and analysis presented.
• A comprehensive comparison on Nash equilibrium algorithms in the literature over different kinds of games.
• ...

Majorization–minimization (MM) is a versatile optimization technique that operates on surrogate functions satisfying tangency and domination conditions. Our focus is on differentiable optimization using inexact MM with quadratic surrogates, which ...

This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on m identical machines. The main result is an O(1) competitive deterministic algorithm for any number of ...$\mathrm{}$

We investigate how the complexity of Euclidean TSP for point sets P inside the strip $(-\infty ,+\infty )\times [0,\delta ]$ depends on the strip width $\delta$. We obtain two main results.

• For the case where the points have distinct integer x-coordinates, we prove that a shortest ...

Submodular maximization is a NP-hard combinatorial optimization problem regularly used in machine learning and data mining with large-scale data sets. To quantify the running time of approximation algorithms, the query complexity and adaptive ...

We present an accelerated or “look-ahead” version of the Newton–Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current iterate and the ...

We study several variants of the problem of moving a convex polytope K, with n edges, in three dimensions through a flat rectangular (and sometimes more general) window. Specifically: (i) We study variants where the motion is restricted to ...${}^{\mathrm{}\mathrm{}}$$\mathrm{}{}_{\mathrm{}}\mathrm{}{}_{\mathrm{}}\mathrm{}$$\mathrm{}$${}_{\mathrm{}}\mathrm{}$${}_{\mathrm{}}{}_{\mathrm{}}$${}_{\mathrm{}}$${}^{\mathrm{}}$

• We firstly give an analysis solution of the proximal operator of the L1 over Linf in compressed sensing.

In this paper, we study minimization of the ratio of ℓ 1 and ℓ ∞ norms (ℓ 1 / ℓ ∞) as a nonconvex and sparsity-promoting metric for solving the unconstrained compressed sensing problems. To design some efficient algorithms, we derive a ...

A tournament is an orientation of a graph. Each edge is a match, directed towards the winner. The score sequence lists the number of wins by each team. In this article, by interpreting score sequences geometrically, we generalize and extend ...

Let G be an intersection graph of n geometric objects in the plane. We show that a maximum matching in G can be found in $O({\rho }^{3\omega /2}{n}^{\omega /2})$ time with high probability, where $\rho$ is the density of the geometric objects and $\omega >2$ is a constant such that $n\times n$ ...${}^{}$${}^{\mathrm{}}$$\mathrm{}\mathrm{}$${\mathrm{}}^{\mathrm{}}{}^{\mathrm{}}{\mathrm{}}^{\mathrm{}}{}^{\mathrm{}}$

A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear ...

We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems. The input to the Weighted Diverse Bases problem consists of a matroid $M$, a weight function $\omega :E(M)\to \mathbb{N}$, and integers $k\ge 1,d\ge 1$...$$${}_{\mathrm{}}{}_{}$$$$$${}_{\mathrm{}}{}_{\mathrm{}}$$$$\mathbb{}$$\mathrm{}\mathrm{}$$$${}_{\mathrm{}}{}_{}$${}_{\mathrm{}}$${}_{\mathrm{}}$$$$$$\mathrm{}\mathrm{}$$$$$${}_{\mathrm{}}{}_{}$$$$\mathsf{}\mathsf{}$$\mathsf{}$$$$$

A k-submodular function is a generalization of a submodular function. The definition domain of a k-submodular function is a collection of k-disjoint subsets instead of simple subsets of ground set. In this paper, we consider the maximization of a ...$\frac{\mathrm{}}{\mathrm{}}\mathrm{}{}^{\mathrm{}}$$\frac{\mathrm{}}{\mathrm{}}\mathrm{}{}^{\mathrm{}}$

We design and analyze an algorithm for computing solutions with coefficients in a finite field F q of underdetermined systems defined over F q. The algorithm is based on reductions to zero-dimensional searches. The searches are performed on “...