A MARKOVIAN ALGORITHM FOR STRICTLY CONCAVE PROGRAMMING WITH LINEAR CONSTRAINTS

1966 ◽  
Author(s):  
Arthur M. Geoffrion
Keyword(s):  
Linear Constraints ◽  
Concave Programming

scholarly journals On two problems over polyhedral convex sets

2015 ◽  
Vol 1 (1) ◽  
pp. 9-15
Author(s):  
Tran Vu Thieu
Keyword(s):  
Convex Sets ◽  
Convex Set ◽  
Linear Constraints ◽  
Concave Programming ◽  
Linear Equality ◽  
Polyhedral Convex ◽  
Polyhedral Convex Sets ◽  
Polyhedral Convex Set

In this paper, we are concerned with the following two problems often encountered in concave programming: Given the  vertices and extreme detections of a polyhedral convex set Modefined by a system of linear constraints, determine the vertices and  extreme directions of the polyhedral convex set  obtained from M just by adding one new linear equality (or inequality) constraint.Among the constraints of a given polyhedral convex set, find those which are redundant, i.e. which can be removed without affecting the polyhedral convex set.

Sampling from Gaussian Markov random fields conditioned on linear constraints

2008 ◽  
Vol 48 ◽  
pp. 1041 ◽  
Author(s):  
Daniel Peter Simpson ◽  
Ian W. Turner ◽  
A. N. Pettitt
Keyword(s):  
Random Fields ◽  
Markov Random Fields ◽  
Linear Constraints ◽  
Gaussian Markov Random Fields ◽  
Markov Random

scholarly journals Towards efficient verification of population protocols

2021 ◽  
Author(s):  
Michael Blondin ◽  
Javier Esparza ◽  
Stefan Jaax ◽  
Philipp J. Meyer
Keyword(s):  
Linear Constraints ◽  
Computational Power ◽  
High Complexity ◽  
Reachability Problem ◽  
Population Protocols ◽  
Finite State ◽  
State Agents ◽  
Efficient Verification ◽  
Primitive Recursive ◽  
Very High

AbstractPopulation protocols are a well established model of computation by anonymous, identical finite-state agents. A protocol is well-specified if from every initial configuration, all fair executions of the protocol reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is -hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class $${ WS}^3$$ WS 3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that $${ WS}^3$$ WS 3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for $${ WS}^3$$ WS 3 reduce to solving boolean combinations of linear constraints over $${\mathbb {N}}$$ N . This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.

scholarly journals Passive Model Predictive Control on a Two-Body Self-Referenced Point Absorber Wave Energy Converter

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1731
Author(s):  
Dan Montoya ◽  
Elisabetta Tedeschi ◽  
Luca Castellini ◽  
Tiago Martins
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Wave Energy ◽  
Power Flow ◽  
Linear Constraints ◽  
Wave Energy Converter ◽  
Control Technique ◽  
Computational Time ◽  
Energy Converter ◽  
Point Absorber

Wave energy is nowadays one of the most promising renewable energy sources; however, wave energy technology has not reached the fully-commercial stage, yet. One key aspect to achieve this goal is to identify an effective control strategy for each selected Wave Energy Converter (WEC), in order to extract the maximum energy from the waves, while respecting the physical constraints of the device. Model Predictive Control (MPC) can inherently satisfy these requirements. Generally, MPC is formulated as a quadratic programming problem with linear constraints (e.g., on position, speed and Power Take-Off (PTO) force). Since, in the most general case, this control technique requires bidirectional power flow between the PTO system and the grid, it has similar characteristics as reactive control. This means that, under some operating conditions, the energy losses may be equivalent, or even larger, than the energy yielded. As many WECs are designed to only allow unidirectional power flow, it is necessary to set nonlinear constraints. This makes the optimization problem significantly more expensive in terms of computational time. This work proposes two MPC control strategies applied to a two-body point absorber that address this issue from two different perspectives: (a) adapting the MPC formulation to passive loading strategy; and (b) adapting linear constraints in the MPC in order to only allow an unidirectional power flow. The results show that the two alternative proposals have similar performance in terms of computational time compared to the regular MPC and obtain considerably more power than the linear passive control, thus proving to be a good option for unidirectional PTO systems.

Sign in / Sign up

Export Citation Format

Share Document