Linear Convergence of Consensus-Based Quantized Optimization for Smooth and Strongly Convex Cost Functions

2020 ◽  
pp. 1-1
Author(s):  
Yuichi Kajiyama ◽  
Naoki Hayashi ◽  
Shigemasa Takai
Keyword(s):  
Linear Convergence ◽  
Cost Functions ◽  
Strongly Convex ◽  
Convex Cost

Cournot Equilibrium Uniqueness: At 0 Discontinuous Industry Revenue and Decreasing Price Flexibility

2019 ◽  
Vol 21 (02) ◽  
pp. 1940010 ◽  
Author(s):  
Pierre Von Mouche ◽  
Takashi Sato
Keyword(s):  
Large Class ◽  
Cost Functions ◽  
Uniqueness Problem ◽  
Unique Equilibrium ◽  
Cournot Equilibrium ◽  
Price Function ◽  
Convex Cost ◽  
Equilibrium Uniqueness ◽  
Price Flexibility

We consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and a proper price function [Formula: see text] with decreasing price flexibility. This class allows for (at [Formula: see text]) discontinuous industry revenue and in particular for [Formula: see text]. The paper illustrates in an exemplary way the Selten–Szidarovszky technique based on virtual backward reply functions. An algorithm for the calculation of the unique equilibrium is provided.

scholarly journals Accelerated Incremental Gradient Descent using Momentum Acceleration with Scaling Factor

2019 ◽  
Author(s):  
Yuanyuan Liu ◽  
Fanhua Shang ◽  
Licheng Jiao
Keyword(s):  
Gradient Descent ◽  
Linear Convergence ◽  
Strongly Convex ◽  
Convex Problems ◽  
Accelerated Methods ◽  
Gradient Descent Methods ◽  
Gradient Descent Algorithm ◽  
Oracle Complexity ◽  
Incremental Gradient Descent ◽  
Theoretical Results

Recently, research on variance reduced incremental gradient descent methods (e.g., SAGA) has made exciting progress (e.g., linear convergence for strongly convex (SC) problems). However, existing accelerated methods (e.g., point-SAGA) suffer from drawbacks such as inflexibility. In this paper, we design a novel and simple momentum to accelerate the classical SAGA algorithm, and propose a direct accelerated incremental gradient descent algorithm. In particular, our theoretical result shows that our algorithm attains a best known oracle complexity for strongly convex problems and an improved convergence rate for the case of n>=L/\mu. We also give experimental results justifying our theoretical results and showing the effectiveness of our algorithm.

scholarly journals PERT scheduling with convex cost functions

2003 ◽  
Vol 292 (1) ◽  
pp. 145-164 ◽  
Author(s):  
Philippe Chrétienne ◽  
Francis Sourd
Keyword(s):  
Cost Functions ◽  
Convex Cost
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