An optimization problem with a piecewise linear objective and conditional threshold constraints. Solution by partitioning

2006 ◽  
pp. 87-98
Author(s):  
B. Lemaire ◽  
C. Lemaire-Misonne
Keyword(s):  
Optimization Problem ◽  
Piecewise Linear

ON CALCULATION OF LINEAR RESOURCE PLANNING MODELS FOR OPTIMAL PROJECT SCHEDULING

2008 ◽  
Vol 13 (2) ◽  
pp. 275-288
Author(s):  
Andrey Valuev
Keyword(s):  
Linear Form ◽  
Project Scheduling ◽  
Resource Sharing ◽  
Optimization Problem ◽  
Piecewise Linear ◽  
Iteration Process ◽  
Resource Planning ◽  
Standard Case ◽  
Decomposition Approach ◽  
Planning Models

Recent author's papers have shown new opportunities resulting from the treatment of resource planning in project scheduling as the optimization problem for a hybrid system. This approach gives the possibility to work out the optimum resource sharing in an iteration process of branch‐and‐bound type. The present paper concentrates on the most standard case of the problem in question for which all the relationships may be represented in the linear form. Two exact finite methods are proposed. The first method is obtained using the piecewise‐linear form of Bellman function, the second evolves from the decomposition approach for dynamic linear programming problem.

scholarly journals Proliferation of non-linear excitations in the piecewise-linear perceptron

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Antonio Sclocchi ◽  
Pierfrancesco Urbani
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Hard Spheres ◽  
Piecewise Linear ◽  
Power Laws ◽  
Universality Class ◽  
Local Minima ◽  
Convex Optimization Problem ◽  
Non Linear ◽  
The Cost

We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

Chaos in a manifold piecewise linear system

1981 ◽  
Vol 64 (10) ◽  
pp. 9-17 ◽  
Author(s):  
Toshimichi Saito ◽  
Hiroichi Fujita
Keyword(s):  
Linear System ◽  
Piecewise Linear ◽  
Piecewise Linear System

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

TAPPI Journal ◽  
2019 ◽  
Vol 18 (10) ◽  
pp. 607-618
Author(s):  
JÉSSICA MOREIRA ◽  
BRUNO LACERDA DE OLIVEIRA CAMPOS ◽  
ESLY FERREIRA DA COSTA JUNIOR ◽  
ANDRÉA OLIVEIRA SOUZA DA COSTA
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Kraft Pulping ◽  
Steam Temperature ◽  
Input Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Multiple Effect ◽  
Sensibility Analysis ◽  
Exergetic Analysis

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

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