The cooccurrence of HIV and unintended pregnancy has prompted a body of work on dual protection, the simultaneous protection against HIV and unintended pregnancy. This study examines dual protection and dual methods as a risk-reduction strategy for women living with HIV. Data are from a cross-sectional sample of HIV-positive women attended in Specialized STI/AIDS Public Health Service Clinics i...

Given a convex optimization problem and its dual, there are many possible firstorder algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is done through convex duality and implies notably that for certain problems, such as for supervised machine learning problems with nonsmooth losses or problems ...

We study a lattice model of interacting loops in three dimensions with a 1/r2 interaction. Using Monte Carlo methods, we have found that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly...

In this paper we propose a method for optimization of fixed polarity arithmetic expressions (FPAEs) based on dual polarity. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using dual polarity route. Conversion from one FPAE to another one is carried out using one-bit checking i....

This paper presents a new regular expression matching method by using Dual Glushkov NFA. Dual Glushkov NFA is the variant of Glushkov NFA, and it has the strong property that all the outgoing transitions to a state of it have the same labels. We propose the new matching method Look Ahead Matching that suited to Dual Glushkov NFA structure. This method executes NFA simulation with reading two in...

The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed within the framework of the line search strategy. We show the global convergence property of our method.

The application of the fast gradient method to the dual QP leads to the Dual Fast Projected Gradient (DFPG) method. The DFPG converges with O ( k−2 ) rate, where k > 0 is the number of steps. At each step, it requires O(nm) operations. Therefore for a given ε > 0 an ε-approximation to the optimal dual function value

We consider a Primal-Dual Augmented Lagrangian (PDAL) method for optimization problems with equality constraints. Each step of the PDAL requires solving the Primal-Dual linear system of equations. We show that under the standard second-order optimality condition the PDAL method generates a sequence, which locally converges to the primal-dual solution with quadratic rate.