Piecewise-Linear Approximation of Quadratic Problems
نویسنده
چکیده
This report covers the application of a piecewise-linear approximation to a quadratic program, QP. In this case the program is one that solves 3D conformal radiation treatment problem and returns optimal beam weights. Four different methods of approximating the quadratic problem were tested and compared to each other and the original problem. The methods are δ method, λ method, σ method, and γ method.
منابع مشابه
Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program
The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...
متن کاملApproximate nonlinear model predictive control with in situ adaptive tabulation
In situ adaptive tabulation (ISAT) is applied to store and retrieve solutions of nonlinear model predictive control (NMPC) problems. ISAT controls approximation error by adaptively building the database of NMPC solutions with piecewise linear local approximations. Unlike initial state or constraint parameterized constrained quadratic programming (QP) solutions, ISAT approximates NMPC solutions ...
متن کاملApproximate Pareto Optimal Solutions of Multi objective Optimal Control Problems by Evolutionary Algorithms
In this paper an approach based on evolutionary algorithms to find Pareto optimal pair of state and control for multi-objective optimal control problems (MOOCP)'s is introduced. In this approach, first a discretized form of the time-control space is considered and then, a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...
متن کاملQuadratic Data Envelopment Analysis
Data Envelopment Analysis (DEA) provides means for piecewise linear approximation of production functions. To improve the fit to the data we propose to improve the flexibility of the frontier by extending DEA towards a more general piecewise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). In contrast to the linear approximation, the quadratic approximation allows for...
متن کاملThe Reformulation-based αGO Algorithm for Solving Nonconvex MINLP Problems – Some Improvements
The α-reformulation (αR) technique can be used to transform any nonconvex twice-differentiable mixedinteger nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is imp...
متن کامل