Convex Separable Programming

2001 ◽  
pp. 79-90
Author(s):  
Stefan M. Stefanov
Keyword(s):  
Separable Programming

scholarly journals Optimal Organization of a Statewide Livestock Auction Market System: The Case of Tennessee

1987 ◽  
Vol 19 (2) ◽  
pp. 121-131
Author(s):  
Emily A. McClain ◽  
Dan L. McLemore
Keyword(s):  
Programming Model ◽  
The State ◽  
Operating Costs ◽  
Market System ◽  
Separable Programming ◽  
Policy Makers ◽  
Auction Market ◽  
Optimal Organization ◽  
Economies Of Size ◽  
Market Operation

AbstractOptimal sizes, number, and locations of Tennessee livestock auction markets were identified as those which minimize the combined costs of assembling and marketing livestock for the state using a separable programming model. The model includes transportation costs, economies of size in market operation, a proxy for reductions in buyers' operating costs attributable to increasing market volumes, and livestock production density, both in and around the state. The model is sufficiently comprehensive and descriptive to be of practical use by policy makers who influence industry change. Results indicate that a reduction in market numbers would lower combined costs.

scholarly journals A game-theoretic optimisation approach to fair customer allocation in oligopolies

2020 ◽  
Vol 21 (4) ◽  
pp. 1459-1486
Author(s):  
Vassilis M. Charitopoulos ◽  
Vivek Dua ◽  
Jose M. Pinto ◽  
Lazaros G. Papageorgiou
Keyword(s):  
Integer Program ◽  
Linear Constraints ◽  
Nash Bargaining ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Programming Approach ◽  
Theoretic Approach ◽  
Separable Programming ◽  
Process Industries ◽  
Game Theoretic

Abstract Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach.

scholarly journals PERBANDINGAN METODE SEPARABLE PROGRAMMING DAN QUADRATIC PROGRAMMING DALAM PEMECAHAN MASALAH PEMROGRAMAN NONLINIER

2019 ◽  
Vol 8 (4) ◽  
pp. 277
Author(s):  
I GEDE WIKAN ADIWIGUNA ◽  
G.K GANDHIADI ◽  
NI MADE ASIH
Keyword(s):  
Nonlinear Programming ◽  
Quadratic Programming ◽  
Linear Function ◽  
Nonlinear Model ◽  
Simplex Method ◽  
Programming Method ◽  
Single Variable ◽  
Separable Programming ◽  
Quadratic Programming Method

The Separable programming method solves nonlinear programming problems by transforming a nonlinear shape that consists of a single variable into a linear function and resolved by the simplex method. Meanwhile, the quadratic programming method accomplishes the two degrees nonlinear model by transforming the nonlinear shape into linear function with the Kuhn Tucker Conditions and resolved by the simplex Wolfe method. Both of these methods are applied to the Markowitz’s portfolio model, which is to find the proportion of stock funds to obtain maximum profits by combination of three shares, such as BMRI, GGRM, and ICBP. The completion using the quadratic programming method is more effective and efficient with the same optimum value.

Real-Time Powertrain Optimization Strategy for Connected Hybrid Electrical Vehicle

2016 ◽  
Author(s):  
Mohd Azrin Mohd Zulkefli ◽  
Zongxuan Sun
Keyword(s):  
Real Time ◽  
Numerical Solutions ◽  
Computation Time ◽  
Computational Effort ◽  
Linear Functions ◽  
Traffic Information ◽  
Vehicle Speed ◽  
Connected Vehicle ◽  
Optimization Strategy ◽  
Separable Programming

Connected Vehicle (CV) technology, which allows traffic information sharing, and Hybrid Electrical Vehicles (HEV) can be combined to improve vehicle fuel efficiency. However, transient traffic information in CV environment necessitates a fast HEV powertrain optimization for real-time implementation. Model Predictive Control (MPC) with Linearization is proposed, but the computational effort is still prohibitive. The Equivalent Consumption Minimization Strategy (ECMS) and Adaptive-ECMS are proposed to minimize computation time, but unable to guarantee charge-sustaining-operation (CS). Fast analytical result from Pontryagin’s Minimum Principles (PMP) is possible but the input has to be unconstrained. Numerical solutions with Linear Programming (LP) are proposed, but over-simplifications of the cost and constraint functions limit the performance of such methods. In this paper, a nonlinear CS constraint is transformed into linear form with input variable change. With linear input and CS constraints, the problem is solved with Separable Programming by approximating the nonlinear cost with accurate linear piecewise functions which are convex. The piecewise-linear functions introduce new dimensionless variables which are solved as a large-dimension constrained linear problem with efficient LP solvers. Comparable fuel economy with Dynamic Programming (DP) is shown, with maximum fuel savings of 7% and 21.4% over PMP and Rule-Based (RB) optimizations. Simulations with different levels of vehicle speed prediction uncertainties to emulate CV settings are presented.

Decentralization in Separable Programming

Econometrica ◽  
1969 ◽  
Vol 37 (1) ◽  
pp. 73 ◽  
Author(s):  
Paul V. Moeseke ◽  
Guy de Ghellinck
Keyword(s):  
Separable Programming
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