A decomposition method for solving a large-scale sparse system of linear equalities and inequalities by sequential quadratic programming

Cybernetics ◽  
1990 ◽  
Vol 25 (5) ◽  
pp. 654-661
Author(s):  
O. N. Tokareva
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Decomposition Method ◽  
Large Scale ◽  
Sparse System

Sequential Quadratic Programming

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 1-51 ◽  
Author(s):  
Paul T. Boggs ◽  
Jon W. Tolle
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Sequential Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Public Domain ◽  
Large Set ◽  
Constrained Optimization Problems ◽  
Nonlinearly Constrained Optimization

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

scholarly journals Customized Sequential Quadratic Programming for Solving Large-Scale AC Optimal Power Flow

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
mostafa Sahraei-Ardakani
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Optimization Problems ◽  
Test Cases ◽  
Time Limits ◽  
Optimal Power ◽  
Wide Range

After decades of research, efficient computation of AC Optimal Power Flow (ACOPF) still remains a challenge. ACOPF is a nonlinear nonconvex problem, and operators would need to solve ACOPF for large networks in almost real-time. Sequential Quadratic Programming (SQP) is one of the powerful second-order methods for solving large-scale nonlinear optimization problems and is a suitable approach for solving ACOPF with large-scale real-world transmission networks. However, SQP, in its general form, is still unable to solve large-scale problems within industry time limits. This paper presents a customized Sequential Quadratic Programming (CSQP) algorithm, taking advantage of physical properties of the ACOPF problem and the choice of the best performing ACOPF formulation. The numerical experiments suggest that CSQP outperforms commercial and noncommercial nonlinear solvers and solves test cases within the industry time limits. A wide range of test cases, ranging from 500-bus systems to 30,000-bus systems, are used to verify the test results.

scholarly journals Customized Sequential Quadratic Programming for Solving Large-Scale AC Optimal Power Flow

2021 ◽  
Author(s):  
Sayed Abdullah Sadat ◽  
mostafa Sahraei-Ardakani
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Large Scale ◽  
Optimization Problems ◽  
Test Cases ◽  
Time Limits ◽  
Optimal Power ◽  
Wide Range

After decades of research, efficient computation of AC Optimal Power Flow (ACOPF) still remains a challenge. ACOPF is a nonlinear nonconvex problem, and operators would need to solve ACOPF for large networks in almost real-time. Sequential Quadratic Programming (SQP) is one of the powerful second-order methods for solving large-scale nonlinear optimization problems and is a suitable approach for solving ACOPF with large-scale real-world transmission networks. However, SQP, in its general form, is still unable to solve large-scale problems within industry time limits. This paper presents a customized Sequential Quadratic Programming (CSQP) algorithm, taking advantage of physical properties of the ACOPF problem and the choice of the best performing ACOPF formulation. The numerical experiments suggest that CSQP outperforms commercial and noncommercial nonlinear solvers and solves test cases within the industry time limits. A wide range of test cases, ranging from 500-bus systems to 30,000-bus systems, are used to verify the test results.

Sequential Quadratic Programming for Solving Constrained Production Optimization–Case Study From Brugge Field

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 874-884 ◽  
Author(s):  
Vahid Dehdari ◽  
Dean S. Oliver
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Gas Injection ◽  
Inequality Constraints ◽  
Production Optimization ◽  
Base Case ◽  
Optimal Controls ◽  
Nonnegativity Constraints

Summary Normally only approximately 30% of the oil in a reservoir is extracted during primary production, but using secondary-production methods such as water or gas injection, it is often possible to increase that percentage significantly and maintain the production rate of a reservoir over a longer period of time. In reservoirs under water or gas injection, additional gains can be obtained through an efficient strategy for management of front movement and reservoir sweep. The objective of reservoir production optimization is to maximize an outcome such as sweep efficiency or net present value (NPV) through the control of completion rates or pressures. Using optimization methods, it is possible to compute control settings that result in increased oil production and decreased water production compared with production from standard practices. In this paper, we focus on optimization using sequential quadratic programming (SQP) with an ensemble-based approach to estimate the gradient for the optimization. Although uncertainty in reservoir properties is usually important for the computation of optimal controls, here we use a single realization of the reservoir to evaluate the efficiency of the optimization algorithm. The most expensive aspect of gradient-based optimization is usually the computation of gradients. Most practical production-optimization problems involve large-scale, highly complex reservoir models with thousands of constraints, which makes numerical calculation of the gradient time consuming. Here, we use an ensemble-based approach for finding gradients and use localization to improve estimation of the gradient from a small number of realizations. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used for maximizing the objective function, with the Hessian estimated from a sequence of estimates of the gradient. Improving the gradient approximation using localization results in improvement to the Hessian approximation. A second important aspect of the efficiency of the method is the identification of active constraints. In this paper, we use a method for eliminating nonnegativity constraints to decrease computation time and an updating procedure to solve each iteration of SQP much faster than the base case. Both the speed of the algorithm and the final NPV were increased significantly. We evaluate the method by applying it to optimization of control settings in the Brugge field. Brugge is a 3D synthetic model designed by TNO with 20 vertical producers and 10 vertical peripheral water injectors. All of the producers and injectors are smart wells whose downhole chokes must be adjusted to optimize NPV. The total number of completion flow rates to be controlled is 84 at each timestep, with 40 timesteps (every 6 months). There are 1,200 inequality constraints on total well liquid rates and 3,360 nonnegativity constraints on completion liquid rates. There are also inequality constraints on the bottomhole pressure (BHP) for wells at each time period.

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