Related papers: Implementing a smooth exact penalty function for e…

In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…

We consider the problem of minimizing a convex separable objective (as a separable sum of two proper closed convex functions $f$ and $g$) over a linear coupling constraint. We assume that $f$ can be decomposed as the sum of a smooth part…

In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve…

In this article we develop a theory of exact linear penalty functions that generalizes and unifies most of the results on exact penalization existing in the literature. We discuss several approaches to the study of both locally and globally…

We consider the problem of optimizing a grey-box objective function, i.e., nested function composed of both black-box and white-box functions. A general formulation for such grey-box problems is given, which covers the existing grey-box…

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…

We introduce a simple, rigorous, and unified framework for solving nonlinear partial differential equations (PDEs), and for solving inverse problems (IPs) involving the identification of parameters in PDEs, using the framework of Gaussian…

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…

Model predictive control (MPC) has become a hot cake technology for various applications due to its ability to handle multi-input multi-output systems with physical constraints. The optimization solvers require considerable time, limiting…

We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…

Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss,…

In [1], the distributed linear-quadratic problem with fixed communication topology (DFT-LQ) and the sparse feedback LQ problem (SF-LQ) are formulated into a nonsmooth and nonconvex optimization problem with affine constraints. Moreover, a…

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…