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The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…

We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…

In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…

Optimization problems with both control variables and environmental variables arise in many fields. This paper introduces a framework of personalized optimization to han- dle such problems. Unlike traditional robust optimization,…

The set of subsystems of a finite quantum system (with variables in Z(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the (where P(m) is the projector to) obeys a supermodularity inequality,…

This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…

We present probabilistic neural programs, a framework for program induction that permits flexible specification of both a computational model and inference algorithm while simultaneously enabling the use of deep neural networks.…

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…