The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary to employ a positive-de...

In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under framework of difference convex functions (DC) approach, a semi-proximal DC algorithm is proposed for solving relaxation DNN whose subproblems solved by augmented Lagrangian method. We generated sequence converges stationary point corres...

Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When th...

A simple linear averaging of the outputs of several networks as e.g. in bagging 3], seems to follow naturally from a bias/variance decomposition of the sum-squared error. The sum-squared error of the average model is a quadratic function of the weighting factors assigned to the networks in the ensemble 7], suggesting a quadratic programmingalgorithm for nding the \optimal"weighting factors. If ...

abstract different strategies are existed for adjusting with water shortage, of which the strategy of suitable policies adoption by determining optimum production function can be mentioned. water shortage and quality degradation of soil and water resources is one of main factors of production reduction. therefore, this study was carried out for determination of tomato sensitivity coefficients a...

Ha 7] recently introduced the generalized proximal point algorithm for solving the generalized equation. In this note, we present the generalized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that instead of adding a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria ...

We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sit...

Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmic-Sobolev inequalities by Bobkov and Ledoux [6], that are s...

A new algorithm, the dual active set algorithm, is presented for solving a minimization problem with equality constraints and bounds on the variables. The algorithm identifies the active bound constraints by maximizing an unconstrained dual function in a finite number of iterations. Convergence of the method is established, and it is applied to convex quadratic programming. In its implementable...

The restoration problem for Poissonian images, arising in medical and astronomical applications, is an active research area. The associated optimization models are quite challenging since the fidelity term of the problem is not a quadratic function and the regularizer is usually nonsmooth. Recently, the augmented Lagrangian-based alternating direction method has been proposed to solve the total...