Related papers: Lagrange multiplier expressions for matrix polynom…
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…
A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
We consider the problem of massive matrix multiplication, which underlies many data analytic applications, in a large-scale distributed system comprising a group of worker nodes. We target the stragglers' delay performance bottleneck, which…
In the application of the Expectation Maximization algorithm to identification of dynamical systems, internal states are typically chosen as latent variables, for simplicity. In this work, we propose a different choice of latent variables,…
It is known that the multiplication of an $N \times M$ matrix with an $M \times P$ matrix can be performed using fewer multiplications than what the naive $NMP$ approach suggests. The most famous instance of this is Strassen's algorithm for…
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the…
In this paper, we consider the cardinality-constrained optimization problems and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
In this paper, we introduce an Augmented Lagrangian based method to incorporate the multiple objectives (MO) in a search ranking algorithm. Optimizing MOs is an essential and realistic requirement for building ranking models in production.…
The moment sum of squares (moment-SOS) hierarchy produces sequences of upper and lower bounds on functionals of the exit time solution of a polynomial stochastic differential equation with polynomial constraints, at the price of solving…
Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problems are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We propose accelerated versions of the operator Sinkhorn iteration for operator scaling using successive overrelaxation. We analyze the local convergence rates of these accelerated methods via linearization, which allows us to determine the…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…