Related papers: Efficient Algorithm for Solving Hyperbolic Program…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for…
Let $p(x_1,...,x_n) =\sum_{(r_1,...,r_n) \in I_{n,n}} a_{(r_1,...,r_n)} \prod_{1 \leq i \leq n} x_{i}^{r_{i}}$ be homogeneous polynomial of degree $n$ in $n$ real variables with integer nonnegative coefficients. The support of such…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also…
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
Minimizing both the worst-case and average execution times of optimization algorithms is equally critical in real-time optimization-based control applications such as model predictive control (MPC). Most MPC solvers have to trade off…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
Thermodynamic computing has emerged as a promising paradigm for accelerating computation by harnessing the thermalization properties of physical systems. This work introduces a novel approach to solving quadratic programming problems using…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…
In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations…
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…
This paper presents a customized second-order cone programming (SOCP) solver tailored for embedded real-time optimization, which frequently arises in modern guidance and control (G&C) applications. The solver employs a practically efficient…