Related papers: Generating Linear, Semidefinite, and Second-order …
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
We consider the problem of computing optimal experimental design on a finite design space with respect to a compound Bayes risk criterion, which includes the linear criterion for prediction in a random coefficient regression model. We show…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
We investigate the semigroup of integer points inside a convex cone. We extend classical results in integer linear programming to integer conic programming. We show that the semigroup associated with nonpolyhedral cones can sometimes have a…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
In this work, we address the exact D-optimal experimental design problem by proposing an efficient algorithm that rapidly identifies the support of its continuous relaxation. Our method leverages a column generation framework to solve such…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
Large-scale simulation optimization (SO) problems encompass both large-scale ranking-and-selection problems and high-dimensional discrete or continuous SO problems, presenting significant challenges to existing SO theories and algorithms.…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact…
The evaluation of heuristic optimizers on test problems, better known as \emph{benchmarking}, is a cornerstone of research in multi-objective optimization. However, most test problems used in benchmarking numerical multi-objective black-box…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…