A mixed type dual for multiobjective variational problems is formulated. Several duality theorems are established relating properly efficient solutions of the primal and dual variational problems under generalized (F,ρ)-convexity. Static mixed type dual multiobjective problems are particular cases of these problems.  2004 Elsevier Inc. All rights reserved.

The recent approach of solving large scale semidefinite programs with a first order method by minimizing an augmented primal-dual function is extended to doubly nonnegative programs. A key point governing the convergence of this approach are regularity properties of the underlying problem. Regularity of the augmented primal-dual function is established under the condition of uniqueness and stri...

We propose in this paper an inexact dual gradient algorithm based on augmented Lagrangian theory and inexact information for the values of dual function and its gradient. We study the computational complexity certification of the proposed method and we provide estimates on primal and dual suboptimality and also on primal infeasibility. We also discuss implementation aspects of the proposed algo...

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Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach tostudy a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain dualityresults. We generate the duality results using exponential membership and non-membership functions to represent thedecision maker’s satisfaction and dissatisfacti...

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we...

To integer programming, a ideals have been problems, which Hiroki Nakayama The University of Tokyo (Received October 27, 2003) Hiroshi Imai jases and standard pairs via toric ilgebraic approaches using Grobner k studied in recent years. In this paper, we consider a unimodular case, e.g., network flow enables us to analyze primal and dual problems in an equal setting. By combining existing resul...

We introduce a new barrier function to solve a class of Semidefinite Optimization Problems (SOP) with bounded variables. That class is motivated by some (SOP) as the minimization of the sum of the first few eigenvalues of symmetric matrices and graph partitioning problems. We study the primal-dual central path defined by the new barrier and we show that this path is analytic, bounded and that a...

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the ...

Lagrangian relaxation is commonly used to generate bounds for mixed-integer linear programming problems. However, when the number of dualized constraints is very large (exponential in the dimension of the primal problem), explicit dualization is no longer possible. In order to reduce the dual dimension, different heuristics were proposed. They involve a separation procedure to dynamically selec...