Oprea proves that Ric(X) ≤ n−1 4 (c + n||H||) improving the Chen-Ricci inequality for Lagrangian submanifolds in complex space forms by using an optimization technique. In this article, we give an algebraic proof of the inequality and completely classify Lagrangian submanifolds in complex space forms satisfying the equality, which is not discussed in Oprea’s paper.

in this article, modeling and optimization of power consumption of two–stage compressed airsystem has been investigated. to do so, the two – stage compressed air cycle with intercooler offajr petroleum company was considered. this cycle includes two centrifugal compressors, ashell, and a tube intercooler. for modeling of power consumption, actual compressors isentropicefficiencies and intercool...

e-mail: [email protected] Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finall...

We develop a new approach towards error control and adaptivity for nite element discretizations in optimization problems governed by partial diierential equations. Using the Lagrangian formalism the goal is to compute stationary points of the rst-order necessary opti-mality conditions. The mesh adaptation is driven by residual-based a posteriori error estimates derived by duality arguments. Thi...

A central problem of branch and bound methods for global optimization is that lower bounds are often not exact even if the diameter of the subdivided regions shrinks to zero This can lead to a large number of subdivisions preventing the method from terminating in reasonable time For the all quadratic optimization problem with convex constraints we present locally exact lower bounds and optimali...

This paper presents Chemo-tactic PSO-DE (CPSO-DE) optimization algorithm combined with Lagrange Relaxation method (LR) for solving Unit Commitment (UC) problem. The proposed approach employs Chemo-tactic PSO-DE algorithm for optimal settings of Lagrange multipliers. It provides high-quality performance and reaches global solution and is a hybrid heuristic algorithm based on Bacterial Foraging O...

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? ...

The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the Lagrangian L(v, x, t) from the set of orbits in Rn to a set of measure-valued orbits. The Eulerian, dual formulation leads an optimization problem on the set of sub-solutions of the corresponding Hamilton-Jacobi equation. Finally, the Monge proble...

We study Ε-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of Ε-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the Ε-Henig saddle point of the Lagrangian set-value...

We consider multistage stochastic optimization models containing nonconvex constraints, e.g., due to logical or integrality requirements. We study three variants of Lagrangian relaxations and of the corresponding decomposition schemes, namely, scenario, nodal and geographical decomposition. Based on convex equivalents for the Lagrangian duals, we compare the duality gaps for these decomposition...