What are Math Optimization Problems?

Finding the optimal objective value for a math model.

Mathematically speaking an Optimization problem consists of one's equations plus an objective function. A solver will tweak all available parameters in a program until the solver finds an optimal objective value. Quick and accurate solutions. Try solving your problem in an Optimization setting. Its great!

Calculus-level programming solves Optimization Problems

If a solution exists, Calculus programming can find it. Say your math model is y = f(x; a, b, c) and you want to find your parameters a, b, & c that maximize Y at X=3. Calculus programming has a find statement that handles this quite nicely. A few runs should convince you on the solution or that your math model needs improving.

Calculus programming allows nesting of Optimization problems.

Optimization Examples:

Problem-Solving Applications include:

CurvFit: a curve fitting program with Lorentzian, Sine, Exponential and Power series are available models to match your data.

Match-n-Freq: a Matched Filter program used to filter signals and slim pulses.

Industry Problem-Solving Descriptions include:

Electrical Filter Design: find the transfer function's poles & zeros; H(s) = Yout(s) / Yin(s).

Pulse Slimming to minimize InterSymbol Interference: via Arbitrary Equalization with Simple LC Structures to reduce errors.

Voice Coil Motor: basically an electromagnetic transducer in which a coil placed in a magnetic pole gap experiences a force proportional to the current passing through the coil.

AC Motor Design: a simulation program for A.C. motor design that was reapplied as a constrained optimization problem with 12 unknown parameters and 7 constraints.

Digitized Signal from Magnetic Recording: Magnetic recording of transitions written onto a computer disc drive may produce an isolated pulse as shown.

PharmacoKinetics: an open-two- compartment model with first order absorption into elimination from central compartment is presented here.

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Textbooks - Parameter Estimation 4 ODE/PDE - Signal Analysis / Spectral Estimation - Body Plasma - Solar Cell
Increasing Productivity Examples: AC Motor Design - Matched Filters - Pulse Slimming / InterSymbol Interference - Pilot (safe) Ejection - PharmacoKinetics Simulation - Poisson's (Differential) Equation - Schrodinger (Differential) Equation - BVP 4 PDE Equations - Implicit (Differential) Equations