Related papers: Efficient Algorithm for Solving Hyperbolic Program…
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…
The Densest Subgraph Problem (DSP) is widely used to identify community structures and patterns in networks such as bioinformatics and social networks. While solvable in polynomial time, traditional exact algorithms face computational and…
This paper proposes a learning-based approach to accelerate the interior-point method (IPM) for solving optimal power flow (OPF) problems by learning the structure of the IPM central path from its early stable iterations. Unlike traditional…
This paper focuses on the study of a mathematical program with equilibrium constraints, where the objective and the constraint functions are all polynomials. We present a method for finding its global minimizers and global minimum using a…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
We present an efficient algorithm to multiply two hyperbolic octonions. The direct multiplication of two hyperbolic octonions requires 64 real multiplications and 56 real additions. More effective solutions still do not exist. We show how…
Second-order cone programs (SOCPs) with quadratic objective functions are common in optimal control and other fields. Most SOCP solvers which use interior-point methods are designed for linear objectives and convert quadratic objectives…
The theory of $n$-fold integer programming has been recently emerging as an important tool in parameterized complexity. The input to an $n$-fold integer program (IP) consists of parameter $A$, dimension $n$, and numerical data of binary…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
We extend our previous algorithm computing the minimum orbital intersection distance (MOID) to include hyperbolic orbits, and mixed combinations ellipse--hyperbola. The MOID is computed by finding all stationary points of the distance…
Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…
We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of…
A new algorithm is derived for computing the actions $f(tA)B$ and $f(tA^{1/2})B$, where $f$ is cosine, sinc, sine, hyperbolic cosine, hyperbolic sinc, or hyperbolic sine function. $A$ is an $n\times n$ matrix and $B$ is $n\times n_0$ with…
In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP)…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain…
We describe a new incomplete but terminating method for real root finding for large multivariate polynomials. We take an abstract view of the polynomial as the set of exponent vectors associated with sign information on the coefficients.…
We present a method that integrates any quantum algorithm capable of finding solutions to integer linear programs into the Branch-and-Price algorithm, which is regularly used to solve large-scale integer linear programs with a specific…
Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…