Related papers: Naive constant rank-type constraint qualifications…

The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…

We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…

The recent success of neural networks in pattern recognition and classification problems suggests that neural networks possess qualities distinct from other more classical classifiers such as SVMs or boosting classifiers. This paper studies…

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better…

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 discuss a weak constraint qualification for conic linear programs and its applications for a few classes of cones. This constraint qualification is used to give a solution to a problem proposed by Shapiro and Z\v{a}linescu and show that…

This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…

In this paper, we are concerned with stationarity conditions and qualification conditions for optimization problems with disjunctive constraints. This class covers, among others, optimization problems with complementarity, vanishing, or…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive several second-order optimality conditions for a local and a…

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…

This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…

In this paper, we propose a new convergent conic programming hierarchy of relaxations involving both semi-definite cone and second-order cone constraints for solving nonconvex polynomial optimization problems to global optimality. The…

Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…

Thanks to the test function of Bian-Guan[2], we successfully obtain a constant rank theorem for partial convex solutions of a class partial differential equations. This is the microscopic version of the macroscopic partial convexity…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

We introduce a quadratically convergent semismooth Newton method for nonlinear semidefinite programming that eliminates the need for the generalized Jacobian regularity, a common yet stringent requirement in existing approaches. Our…