in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

The geometric duality theory of Heyde and Löhne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson’s outer approximation method (Benson, 1998a,b) while the dual problem can be solved by a dual variant of Benson’s algorithm (Ehrgott et al., 2007). Duality theory then assures that it is possible to find the nondomi...

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...

The primal–dual method is a powerful algorithmic technique that has proved to be extremely useful for a wide variety of problems in the area of approximation algorithms for NP-hard problems. The method has its origins in the realm of exact algorithms, e.g., for matching and network flow. In the area of approximation algorithms, the primal–dual method has emerged as an important unifying design ...

Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDP’s. However, primal–dual codes have had some trouble in solving larger problems because of the storage requirements and required computational effort. In this paper we de...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov’s excessive gap technique in a structured fashion and unifies it with smoothing and primal-dual...

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal problem that minimizes cost over finite time horizon for stochastic systems subject energy constraints. To tackle problem, propose efficient bisection line search algorithm outperforms other approaches such as semidefinite programming in terms comp...

In this paper we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions the error bounds for the primal and dual sequences converge to zer...