In this paper, we consider an interior point method for nonlinear semidefinite programming. Yamashita, Yabe and Harada presented a primal-dual interior point method in which a nondifferentiable merit function was used. By using shifted barrier KKT conditions, we propose a differentiable primal-dual merit function within the framework of the line search strategy, and prove the global convergence...

We consider the total variation minimization model with consistent finite element discretization. It has been shown in the literature that this model can be reformulated as a saddle-point problem and be efficiently solved by the primal-dual method. The convergence for this application of the primal-dual method has also been analyzed. In this paper, we focus on a more general primaldual scheme w...

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to bot...

We present primal-dual decomposition algorithms for convex optimization problems with cost functions f(x) + g(Ax), where f and g have inexpensive proximal operators and A can be decomposed as a sum of two structured matrices. The methods are based on the Douglas–Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image ...

In a soft environment, we investigated several (classical) structures such as ideals, filters, grills, etc. It is well known that these are applied to expand abstract concepts; in addition, some of them offer vital tool address practical issues, especially those related improving rough approximation operators and accuracy measures. Herein, contribute this line research by presenting novel type ...

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although LP models require well-suited information and precise data, managers and decision makers dealing with optimization problems often have a lack of information on the exact values of some parameters used in their models. Fuzzy sets provide a power...

In a recent paper [8], Chan and Sun reported for semidefinite programming (SDP) that the primal/dual constraint nondegeneracy is equivalent to the dual/primal strong second order sufficient condition (SSOSC). This result is responsible for a number of important results in stability analysis of SDP. In this paper, we study duality of this type in nonlinear semidefinite programming (NSDP). We int...

Our goal is to establish an efficient decomposition of an ideal A of a commutative ring R as an intersection of primal ideals. We prove the existence of a canonical primal decomposition: A = ⋂ P∈XA A(P ), where the A(P ) are isolated components of A that are primal ideals having distinct and incomparable adjoint primes P . For this purpose we define the set Ass(A) of associated primes of the id...

Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? ...