Related papers: An active-set algorithm for norm constrained quadr…
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…
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…
We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…
In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We prove that the active-set method needs an exponential number of iterations in the worst-case to maximize a convex quadratic function subject to linear constraints, regardless of the pivot rule used. This substantially improves over the…
We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the…
In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the…
In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, $L_{q}$ regularization with $q\in(0,1)$) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency.…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Abstracting neural networks with constraints they impose on their inputs and outputs can be very useful in the analysis of neural network classifiers and to derive optimization-based algorithms for certification of stability and robustness…
Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…