Related papers: A Combinatorial Algorithm to Compute Regularizatio…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different…
In the past decade, many parameterized algorithms were developed for packing problems. Our goal is to obtain tradeoffs that improve the running times of these algorithms at the cost of computing approximate solutions. Consider a packing…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
Latent variable models are a fundamental modeling tool in machine learning applications, but they present significant computational and analytical challenges. The popular EM algorithm and its variants, is a much used algorithmic tool; yet…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…
Within machine learning model evaluation regimes, feature selection is a technique to reduce model complexity and improve model performance in regards to generalization, model fit, and accuracy of prediction. However, the search over the…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
We consider the problem of computing sample points in each connected component of a semi-algebraic set defined by the non-vanishing or the positivity of an n-variate polynomial of degree d, with rational coefficients of bit size bounded by…
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact…
A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
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…
Within a statistical learning setting, we propose and study an iterative regularization algorithm for least squares defined by an incremental gradient method. In particular, we show that, if all other parameters are fixed a priori, the…