Level set methods for optimization problems involving geometry and constraints II. Optimization over a fixed surface
نویسندگان
چکیده
منابع مشابه
Level set methods for optimization problems involving geometry and constraints II. Optimization over a fixed surface
In this work, we consider an optimization problem described on a surface. The approach is illustrated on the problem of finding a closed curve whose arclength is as small as possible while the area enclosed by the curve is fixed. This problem exemplifies a class of optimization and inverse problems that arise in diverse applications. In our approach, we assume that the surface is given parametr...
متن کاملLEVEL SET METHODS FOR OPTIMIZATION PROBLEMS INVOLVING GEOMETRY AND CONSTRAINTS II. OPTIMIZATION OVER A FIXED SURFACE By
In this work, we consider an optimization problem described on a surface. The approach is illustrated on the problem of finding a closed curve whose arclength is as small as possible while the area enclosed by the curve is fixed. This problem exemplifies a class of optimization and inverse problems that arise in diverse applications. In our approach, we assume that the surface is given parametr...
متن کاملA BINARY LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION
This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...
متن کاملLevel-set methods for convex optimization
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric level-set problems. A zero-finding procedure, base...
متن کاملPart I: Methods Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set
We present a unified approach to a class of nonconvex global optimization problems with composite monotonic constraints. (By composite monotonic function is meant a function which is the composition of a monotonic function on R n with a mapping from R n → R m with m ≤ n.) This class includes problems with constraints involving products of linear functions, sums of ratio functions, etc., and als...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2008
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2008.07.011