Approximate affine linear relationship between L-1 norm objective functional values and L-2 norm constraint bounds

作者：Yang, Zhijing; Ling, Bingo Wing Kuen^*; Bingham, Chris

来源：IET Signal Processing, 2015, 9(9): 670-680.

DOI：10.1049/iet-spr.2014.0402

• signal representation
• compressed sensing
• linear programming
• L-2 norm constraint bound
• L-1 norm objective functional value
• approximate affine linear relationship
• optimisation problem
• sparse signal representation

For an optimisation problem with an L-1 norm objective function subject to an L-2 norm inequality constraint, this study shows that there is an approximately linear relationship between the L-1 norm objective functional values and the L-2 norm specifications. This relationship is verified through the use of random and real world industrial data. The obtained results can be employed for (i) estimating the L-1 norm objective functional value without solving the optimisation problem numerically; (ii) providing an insight for defining the L-2 norm specification in which a simple method is proposed in this study; and (iii) testing whether the obtained solutions are the globally optimal solutions or not. These advantages are demonstrated via the use of random data.

• 出版日期2015-12
• 单位广东工业大学