Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respe...

Regularized empirical risk minimization problems are fundamental tasks in machine learning and data analysis. Many successful approaches for solving these problems are based on a dual formulation, which often admits more efficient algorithms. Often, though, the primal solution is needed. In the case of regularized empirical risk minimization, there is a convenient formula for reconstructing an ...

To obtain high-quality segmentation results the integration of semantic information is indispensable. In contrast to existing segmentation methods which use a spatial regularizer, i.e. a local interaction between image points, the co-occurrence prior [15] imposes penalties on the co-existence of different labels in a segmentation. We propose a continuous domain formulation of this prior, using ...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...

Report The aim of this work is to make some investigations concerning duality for mul-tiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, unde...

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method ...

The primal-dual method increases the dual variables gradually until some dual constraint becomes tight. Then, the primal variable corresponding to the tight dual constraint is ‘bought’ (or selected), and the process continues till we get a feasible primal solution. Next, we compare the value of the primal solution to the value of the dual solution to get an appropriate approximation factor (or ...

As is well known, Q-superlinear or Q-quadratic convergence of the primal-dual sequence generated by an optimization algorithm does not, in general, imply Q-superlinear convergence of the primal part. Primal convergence, however, is often of particular interest. For the sequential quadratic programming (SQP) algorithm, local primal-dual quadratic convergence can be established under the assumpti...

The purpose of this article is to introduce the concept second order (?,?)-invex function for continuous case and apply it discuss duality relations a class multiobjective variational problem. Weak, strong strict theorems are obtained in relate efficient solutions primal problem its Mond-Weir type dual using aforesaid assumption. A non-trivial example also exemplified show presence proposed fun...

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large machine learning datasets. However, existing implementations communicate at every iteration which, on modern data center and supercomputing architectures, often ...