Related papers: An Exact Algorithm for Optimization Problems with …
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
In this paper, we study convex optimization problems where agents of a network cooperatively minimize the global objective function which consists of multiple local objective functions. Different from most of the existing works, the local…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we study power-efficient resource allocation for multicarrier non-orthogonal multiple access (MC-NOMA) systems. The resource allocation algorithm design is formulated as a non-convex optimization problem which jointly designs…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, computational statistics, and computer science. In this paper,…
Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver NExOS…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
This paper mainly addresses the distributed online optimization problem where the local objective functions are assumed to be convex or non-convex. First, the distributed algorithms are proposed for the convex and non-convex situations,…