Related papers: Continuous iterative algorithms for anti-Cheeger c…

We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut…

We propose a new algorithm for finite sum optimization which we call the curvature-aided incremental aggregated gradient (CIAG) method. Motivated by the problem of training a classifier for a d-dimensional problem, where the number of…

The combinatorial integral approximation (CIA) is a solution technique for integer optimal control problems. In order to regularize the solutions produced by CIA, one can minimize switching costs in one of its algorithmic steps. This leads…

The first nontrivial lower bound of the worst-case approximation ratio for the maxcut problem was achieved via the dual Cheeger problem, whose optimal value is referred to the dual Cheeger constant $h^+$, and later improved through its…

This paper presents a detailed review of both theory and algorithms for the Cheeger cut based on the graph $1$-Laplacian. In virtue of the cell structure of the feasible set, we propose a cell descend (CD) framework for achieving the…

In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data…

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum…

We propose to generate Lagrangian cut for two-stage stochastic integer program by batch, in contrast to the existing methods which solve each Lagrangian subproblem at every iteration. We establish two convergence properties of the proposed…

This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on…

Cellular automata are capable of developing complex behaviors based on simple local interactions between their elements. Some of these characteristics have been used to propose and improve meta-heuristics for global optimization; however,…

Chvatal-Gomory cutting planes (CG-cuts for short) are a fundamental tool in Integer Programming. Given any single CG-cut, one can derive an entire family of CG-cuts, by `iterating' its multiplier vector modulo one. This leads naturally to…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…

Deep CCA is a recently proposed deep neural network extension to the traditional canonical correlation analysis (CCA), and has been successful for multi-view representation learning in several domains. However, stochastic optimization of…

Competitive equilibrium (CE) for chores has recently attracted significant attention, with many algorithms proposed to approximately compute it. However, existing algorithms either lack iterate convergence guarantees to an exact CE or…

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…

Since numbers in the computer are represented with a fixed number of bits, loss of accuracy during calculation is unavoidable. At high precision where more bits (e.g. 64) are allocated to each number, round-off errors are typically small.…

Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…

We give an improved branch-and-bound solver for the multiterminal cut problem, based on the recent work of Henzinger et al.. We contribute new, highly effective data reduction rules to transform the graph into a smaller equivalent instance.…