Primal-Dual Gradient Structured Functions: Second-Order Results; Links to Epi-Derivatives and Partly Smooth Functions

2003 ◽  
Vol 13 (4) ◽  
pp. 1174-1194 ◽  
Author(s):  
Robert Mifflin ◽  
Claudia Sagastizábal
Keyword(s):  
Second Order ◽  
Smooth Functions ◽  
Primal Dual ◽  
Dual Gradient ◽  
Partly Smooth

scholarly journals The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Ming Huang ◽  
Li-Ping Pang ◽  
Xi-Jun Liang ◽  
Zun-Quan Xia
Keyword(s):  
Optimization Problems ◽  
Optimization Technique ◽  
Second Order ◽  
Performance Criteria ◽  
Dual Function ◽  
Space Decomposition ◽  
Decision Variables ◽  
Primal Dual ◽  
Dual Gradient ◽  
Derivatives Of

We study optimization problems involving eigenvalues of symmetric matrices. We present a nonsmooth optimization technique for a class of nonsmooth functions which are semi-infinite maxima of eigenvalue functions. Our strategy uses generalized gradients and𝒰𝒱space decomposition techniques suited for the norm and other nonsmooth performance criteria. For the class of max-functions, which possesses the so-called primal-dual gradient structure, we compute smooth trajectories along which certain second-order expansions can be obtained. We also give the first- and second-order derivatives of primal-dual function in the space of decision variablesRmunder some assumptions.

Routing Optimization with Efficient Second Order Distributed Approach Using Congestion Control Rules

2017 ◽  
Vol 7 (7) ◽  
pp. 363
Author(s):  
Jaya Pratha Sebastiyar ◽  
Martin Sahayaraj Joseph
Keyword(s):  
Congestion Control ◽  
Second Order ◽  
Back Pressure ◽  
Order Method ◽  
Delay Performance ◽  
Routing Optimization ◽  
Distributed Approach ◽  
Control Rules ◽  
Primal Dual ◽  
Queue Stability

Distributed joint congestion control and routing optimization has received a significant amount of attention recently. To date, however, most of the existing schemes follow a key idea called the back-pressure algorithm. Despite having many salient features, the first-order sub gradient nature of the back-pressure based schemes results in slow convergence and poor delay performance. To overcome these limitations, the present study was made as first attempt at developing a second-order joint congestion control and routing optimization framework that offers utility-optimality, queue-stability, fast convergence, and low delay.  Contributions in this project are three-fold. The present study propose a new second-order joint congestion control and routing framework based on a primal-dual interior-point approach and established utility-optimality and queue-stability of the proposed second-order method. The results of present study showed that how to implement the proposed second-order method in a distributed fashion.

scholarly journals Time-Varying Optimization of LTI Systems via Projected Primal-Dual Gradient Flows

2021 ◽  
pp. 1-1
Author(s):  
Gianluca Bianchin ◽  
Jorge Cortes ◽  
Jorge I. Poveda ◽  
Emiliano Dall'Anese
Keyword(s):  
Time Varying ◽  
Gradient Flows ◽  
Primal Dual ◽  
Dual Gradient

scholarly journals Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1348 ◽  
Author(s):  
Ramu Dubey ◽  
Lakshmi Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Second Order ◽  
Type Model ◽  
Dual Model ◽  
Duality Theorems ◽  
Converse Duality ◽  
Numerical Example ◽  
Primal Dual

In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond–Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.

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