Parameterized image varieties and estimation with bilinear constraints

2003 ◽  
Author(s):  
Y. Genc ◽  
J. Ponce ◽  
Y. Leedan ◽  
P. Meer
Keyword(s):  
Bilinear Constraints

Multiple-Instance Classification via Generalized Eigenvalue Proximal SVM

2010 ◽  
Vol 143-144 ◽  
pp. 1235-1239
Author(s):  
Zhen Wang ◽  
Dong Mei Li
Keyword(s):  
Linear Function ◽  
Classification Problem ◽  
Real Space ◽  
Local Solution ◽  
The Other ◽  
Computational Results ◽  
Finite Dimensional ◽  
Generalized Eigenvalue ◽  
Bilinear Constraints ◽  
Nonparallel Planes

The multiple-instance classification problem is formulated using a linear or nonlinear kernel as the minimization of a linear function in a finite dimensional real space subject to linear and bilinear constraints by SVM-based methods. This paper presents a new multiple-instance classifier that determines two nonparallel planes by solving generalized eigenvalue proximal SVM. Our method converges in a few iterations to a local solution. Computational results on a number of datasets indicate that the proposed algorithm is competitive with the other SVM-based methods in multiple-instance classification.

scholarly journals Innovative Energy Arbitrage Models and Algorithms for Battery Energy Storage Systems in Electricity Market

2021 ◽  
Author(s):  
Ang Li ◽  
Jiming Peng ◽  
Lei Fan ◽  
Pengwei Du
Keyword(s):  
Energy Storage ◽  
Quadratic Programming ◽  
Linear Functions ◽  
Electricity Production ◽  
Programming Approach ◽  
Decision Variable ◽  
Battery Energy Storage ◽  
New Model ◽  
Bilinear Constraints ◽  
Battery Energy

<div>Maintaining the balance between electricity production and consumption is an essential task in the operations of modern power grids. In recent years, battery energy storage system (BESS) has been gaining more and more attention owning to its decreasing capital cost, high flexibility and short response time. However, there exist several technical challenges in developing accurate models and effective algorithms for the operations of BESS. One major challenge is that in order to precisely describe the changing dynamics of battery status, usually highly non-linear functions and integer variables must be used in the model, leading to optimization models with nonlinear and non-convex objective function/constraints that are difficult to handle. To address the above challenges, in this paper we first explore the physical law in the battery charging and discharging process to develop a new model which naturally addresses both the charging and discharging processes through a single current decision variable. Then we propose to approximate the dependency relationship between the open circuit voltage (OCV) and the state of charge (SOC) by some linear functions. This leads to a new non-convex quadratic programming model with linear and bilinear constraints (BLCQP) for the identification of the optimal operational strategy for the BESS. To cope with the bilinear constraints in the BLCQP, we introduce a novel transformation technique to transfer the original BLCQP into another equivalent exponential optimization problem with linear constraints (LCEO). A new sequential linear and quadratic programming approach (SLQP) for the LCEO is developed and its convergence is established. Preliminary experiments are conducted to demonstrate the efficacy of the new model and the efficiency of the new algorithm.</div>

Innovative Energy Arbitrage Models and Algorithms for Battery Energy Storage Systems in Electricity Market

2021 ◽  
Author(s):  
Ang Li ◽  
Jiming Peng ◽  
Lei Fan ◽  
Pengwei Du
Keyword(s):  
Energy Storage ◽  
Quadratic Programming ◽  
Linear Functions ◽  
Electricity Production ◽  
Programming Approach ◽  
Decision Variable ◽  
Battery Energy Storage ◽  
New Model ◽  
Bilinear Constraints ◽  
Battery Energy

<div>Maintaining the balance between electricity production and consumption is an essential task in the operations of modern power grids. In recent years, battery energy storage system (BESS) has been gaining more and more attention owning to its decreasing capital cost, high flexibility and short response time. However, there exist several technical challenges in developing accurate models and effective algorithms for the operations of BESS. One major challenge is that in order to precisely describe the changing dynamics of battery status, usually highly non-linear functions and integer variables must be used in the model, leading to optimization models with nonlinear and non-convex objective function/constraints that are difficult to handle. To address the above challenges, in this paper we first explore the physical law in the battery charging and discharging process to develop a new model which naturally addresses both the charging and discharging processes through a single current decision variable. Then we propose to approximate the dependency relationship between the open circuit voltage (OCV) and the state of charge (SOC) by some linear functions. This leads to a new non-convex quadratic programming model with linear and bilinear constraints (BLCQP) for the identification of the optimal operational strategy for the BESS. To cope with the bilinear constraints in the BLCQP, we introduce a novel transformation technique to transfer the original BLCQP into another equivalent exponential optimization problem with linear constraints (LCEO). A new sequential linear and quadratic programming approach (SLQP) for the LCEO is developed and its convergence is established. Preliminary experiments are conducted to demonstrate the efficacy of the new model and the efficiency of the new algorithm.</div>

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