1. A method comprising creating a non-transitory computer readable design for a circuit having components characterized by one or more design parameters by performing, on a computing device, operations comprising:
generating an optimization problem comprising a set of non-linear constraint functions and a set of linear constraint functions, each constraint function comprising exponent of at least one design parameter, the set of non-linear constraint functions and the set of linear constraint functions describing the circuit’s operation;
converting the optimization problem into a convex optimization problem by taking a logarithm of each of the set of non-linear constraint functions; and
solving the convex optimization problem to produce one or more optimized design parameter values for the circuit.
2. The method of claim 1, wherein the one or more design parameters comprises a set of non-exponential design parameters and a first set of exponential design parameters, wherein the operations further comprise:
replacing the set of non-exponential design parameters with a second set of exponential design parameters; and
rewriting the optimization problem in terms of the first and second set of exponential design parameters.
3. The method of claim 2, wherein the second set of exponential design parameters is obtained by taking a logarithm of each design parameter in the set of non-exponential design parameters.
4. The method of claim 1, wherein the set of non-linear constraint functions comprises at least one of a posynomial function, a monomial function, and a log-convex function.
5. The method of claim 1, wherein the operations further comprise transforming, through approximation, a set of signomial constraint functions into constraint functions that are not signomial.
6. The method of claim 1, wherein the operations further comprise providing constraint values for the constraint functions.
7. The method of claim 1, wherein a set of design parameters for transistors are selected, wherein the transistors comprise Metal-Oxide-Semiconductor (MOS) transistors.
8. The method of claim 7, wherein the set of design parameters comprise any of: (a) a transistor width (W); (b) a transistor length (L); (c) a two-terminal voltage of one of the MOS transistors; and (d) a two-terminal capacitance of one of the MOS transistors.
9. A computer program product stored as program code on a non-transitory computer-readable medium, the program code executable by at least one processor for optimizing a circuit having components characterized by one or more design parameters, the computer program product comprising a computer readable program code comprising instructions for:
generating an optimization problem comprising a set of non-linear constraint functions and a set of linear constraint functions, each constraint function comprising exponent of at least one design parameter, the set of non-linear constraint functions and the set of linear constraint functions describing the circuit’s operation;
converting the optimization problem into a convex optimization problem by taking a logarithm of each of the set of non-linear constraint functions; and
solving the convex optimization problem to produce one or more optimized design parameter values for the circuit.
10. The computer program product of claim 9, wherein the one or more design parameters comprises a set of non-exponential design parameters and a first set of exponential design parameters, wherein the computer readable program code further comprises instructions for:
replacing the set of non-exponential design parameters with a second set of exponential design parameters; and
rewriting the optimization problem in terms of the first and second set of exponential design parameters.
11. The computer program product of claim 10, wherein the second set of exponential design parameters is obtained by taking a logarithm of each design parameter in the set of non-exponential design parameters.
12. The computer program product of claim 9, wherein the set of non-linear constraint functions comprises at least one of a posynomial function, a monomial function, and a log-convex function.
13. The computer program product of claim 9, wherein the computer readable program code further comprises instructions for transforming, through approximation, a set of signomial constraint functions into constraint functions that are not signomial.
14. The computer program product of claim 9, wherein the computer readable program code further comprises instructions for providing constraint values for the constraint functions.
15. A computer having a storage medium containing program code that when processed by a processor of the computer causes a method to optimize a circuit having components characterized by one or more design parameters, the method comprising:
generating an optimization problem comprising a set of non-linear constraint functions and a set of linear constraint functions, each constraint function comprising exponent of at least one design parameter, the set of non-linear constraint functions and the set of linear constraint functions describing the circuit’s operation;
converting the optimization problem into a convex optimization problem by taking a logarithm of each of the set of non-linear constraint functions; and
solving the convex optimization problem to produce one or more optimized design parameter values for the circuit.
16. The computer of claim 15, wherein the one or more design parameters comprises a set of non-exponential design parameters and a first set of exponential design parameters, wherein the method further comprises:
replacing the set of non-exponential design parameters with a second set of exponential design parameters; and
rewriting the optimization problem in terms of the first and second set of exponential design parameters.
17. The computer of claim 16, wherein the second set of exponential design parameters is obtained by taking a logarithm of each design parameter in the set of non-exponential design parameters.
18. The computer of claim 15, wherein the set of non-linear constraint functions comprises at least one of a posynomial function, a monomial function, and a log-convex function.
19. The computer of claim 15, wherein the method further comprises transforming, through approximation, a set of signomial constraint functions into constraint functions that are not signomial.
20. The computer of claim 15, wherein the method further comprises providing constraint values for the constraint functions.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. An implantable catheter for delivering a therapeutic agent to a body, the catheter comprising:
an elongate tubular core comprising a first material, the core having a proximal end and a distal end;
an elongate tubular tip comprising a second material different that the first material, the tip having a bending stiffness greater than a bending stiffness of the core, wherein a proximal end of the tip is positioned to abut or be near the distal end of the core such that a continuous lumen extends from the proximal end of the core to a distal end of the tip, the tip defining a cylindrical outer surface of uniform diameter extending between the proximal and distal ends of the tip; and
an elastomeric jacket having a radial compliance greater than a radial compliance of the core, the elastomeric jacket surrounding and fixedly secured to longitudinal portions of both the tip and the core, wherein the distal end of the tip protrudes beyond a distal end of the elastomeric jacket, and wherein the elastomeric jacket has an outer diameter that is three or more times larger than an outer diameter of the core.
2. The catheter of claim 1, wherein a proximal end of the elastomeric jacket terminates at the proximal end of the core.
3. The catheter of claim 1, further comprising strengthening members positioned near at least a portion of both the core and the tip.
4. The catheter of claim 3, wherein the strengthening members are surrounded by, or embedded within, the elastomeric jacket.
5. The catheter of claim 3, wherein the strengthening members terminate a distance short of the distal end of the elastomeric jacket.
6. The catheter of claim 3, wherein the strengthening members comprise a tubular braid located coaxially about portions of both the core and the tip.
7. The catheter of claim 6, wherein the tubular braid comprises a plurality of polyethylene terepthalate (PET) fibers.
8. The catheter of claim 1, further comprising one or more longitudinal members extending along portions of one or both of the core and the tip.
9. The catheter of claim 1, wherein the core comprises polyetheretherketone (PEEK) tubing.
10. The catheter of claim 1, wherein the tip comprises glass tubing.
11. The catheter of claim 1, wherein the tip comprises stainless steel hypodermic tubing.
12. The catheter of claim 1, wherein the elastomeric jacket comprises a material selected from the group consisting of silicone and polyurethane.
13. The catheter of claim 1, wherein the distal end of the elastomeric jacket comprises a marker band.
14. The catheter of claim 13, wherein the marker band comprises a fluoroscopic or radiopaque material.
15. An implantable catheter for delivering a therapeutic agent to a body, the catheter comprising:
an elongate tubular core comprising a first material, the core having a proximal end and a distal end;
an elongate tubular tip comprising a second material different that the first material, the tip having a bending stiffness greater than a bending stiffness of the core, the tip also having a distal end and a proximal end, wherein the proximal end of the tip is positioned to abut or be near the distal end of the core such that a continuous lumen extends from the proximal end of the core to the distal end of the tip, the tip defining a cylindrical outer surface of uniform diameter extending between the proximal and distal ends of the tip; and
an elastomeric jacket comprising: a proximal end terminating at the proximal end of the core; and a distal end terminating at a location between the proximal and distal ends of the tip, wherein the elastomeric jacket is fixedly secured to outer portions of both the tip and the core, and wherein the elastomeric jacket has an outer diameter that is three or more times larger than an outer diameter of the core.
16. The catheter of claim 15, wherein the outer diameter of the elastomeric jacket is about 4 to about 6 times larger than the outer diameter of the core.
17. The catheter of claim 15, wherein the first material comprises polyetheretherketone (PEEK).
18. The catheter of claim 15, wherein the second material comprises stainless steel.