Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by the second-order integrator, but not for other cases. The difficulty in the problem is that the monotonicity constraint should be satisfied over an interval which has the cardinality of the continuum. To solve this problem,  first formulate the problem as a semi-infinite quadratic programming problem, and then  adopt a discretization technique to obtain a finite-dimensional quadratic programming problem. It is shown that the solution of the finite-dimensional problem always satisfies the infinite-dimensional monotonicity constraint. It is also proved that the approximated solution converges to the exact solution as the discretization grid-size tends to zero. An example is presented to show the effectiveness of the proposed method.
['Masaaki Nagahara', 'Clyde F. Martin']
I am writing a research paper on a idea Monotone Smoothing Splines Using General Linear Systems
[{"from": "human", "value": "I am writing a research paper on a idea Monotone Smoothing Splines Using General Linear Systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract#R##N##R##N#, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by the second-order integrator, but not for other cases. The difficulty in the problem is that the monotonicity constraint should be satisfied over an interval which has the cardinality of the continuum. To solve this problem,  first formulate the problem as a semi-infinite quadratic programming problem, and then  adopt a discretization technique to obtain a finite-dimensional quadratic programming problem. It is shown that the solution of the finite-dimensional problem always satisfies the infinite-dimensional monotonicity constraint. It is also proved that the approximated solution converges to the exact solution as the discretization grid-size tends to zero. An example is presented to show the effectiveness of the proposed method."}]