Supreme Analytical Solutions
Mark L. Stone

Harnessing his M.I.T. Math and Stanford Operations Research education,
Mark L. Stone is an experienced cutting edge Quantitative Analyst


Nonlinear multivariate dynamic stochastic global optimization

(everything else is a special case, an approximation, or a compromise)

Missile Defense

(Mark L. Stone doesn't want a nuclear holocaust. Do you?)

Mark L. Stone's LinkedIn profile

Mark L. Stone's twitter feed

Ultra Trust Region twitter feed
Revolutionary advance invented by Mark L. Stone to make nonlinear optimization solution robust as hell

Ultra Trust Region optimization maximizes mileage per gradient evaluation and
robustifies nonlinear optimization algorithm performance

Nasty non-convex, nonlinear, ill-conditioned functions?
Noisy objective function and gradient evaluations? Not a prob, Bob.

UltraSimOpt twitter feed
World's first robust and reliable constrained stochastic simulation optimizer

Linear (LMI) and Bilinear (BMI) Matrix Inequalities, Nonlinear SDPs?
Go ahead, include these deterministic semidefinite constraints in your
simulation optimization problem. UltraSimOpt loves them.

Robust termination (optimality) criteria handle
linear & smooth nonlinear constraints, linear & nonlinear SDP constraints,
and noisy objective function & gradient evaluation

Uses Ultra Trust regions. Coming soon.

Favorite Web Sites

Moderator and key contributor at CVX Forum (convex optimization tool)

YALMIP Forum (convex and non-convex optimization tool)

Cross Validated Stack Exchange Forum

Operations Research Stack Exchange Forum

Math Overflow (research level) Stack Exchange Forum

Computational Science Stack Exchange Forum

Automatic Differentiation for Matlab (ADiMat). Matrix level reverse mode automatic differentiation allows computing gradient in one fell swoop for use in nonlinear optimization, including Infinitesimal Perturbation Analysis (IPA) gradient of stochastic simulation objective function. (Matrix Calculus) Vector and Matrix Level Symbolic Differentiation in arbitrary (unspecified) dimension (Maple and Mathematica can't do that), based on under the hood tensor formulation. Now what we need is for this capability to be implemented within a Matrix and Tensor level Automatic Differeentiator, preferably in MATLAB (but Python's o.k. too)

Interval Computations Home Page

NETLIB Repository (of mathematical software)

CVXQUAD (Hey, who doesn't like Quantum (Matrix) Relative Entropy?)

Mark L. Stone's CVX Forum post on problem reformulation tricks needed to effectively use CVXQUAD

CPLEX - Mixed-Integer Linear, convex & local/global non-convex Quadratic, and Second Order Cone Programming

MOSEK - Mixed-Integer Linear, convex Quadratic, Second Order Cone, and Exponential Cone Programming; Linear Matrix Inequalities

KNITRO - Mixed-Integer Local Nonlinear Optimization Solver (but no SDP capability, oh well)

BARON - Mixed-Integer Global Nonlinear Optimization Solver (no SDP capability, oh well, but feel free to request it)

PENNON (and PENLAB) - Local Nonlinear SDP (Semidefinite Programming) Solver. Specify it as upper solver under YALMIP's BMIBNB to globally optimize Nonlinear SDPs.

Multiprecision Computing Toolbox for MATLAB (octuple precision comes in handy when performing conditional Multivariate Normal calculations with extremely ill-conditioned covariance matrices)

Mark L. Stone's LinkedIn Article "High Crimes and Misdemeanors in the Analysis Biz, Part 1: My Funny but True Taylor Series Stories"

Mark L. Stone's LinkedIn Article "High Crimes and Misdemeanors in the Analysis Biz, Part 2: Variance is always nonnegative. Or is it?

Mark L. Stone's LinkedIn Article "High Crimes and Misdemeanors in the Analysis Biz, Part 3: The Universal Monte Carlo Simulator. Are 'High Fidelity' Simulations Really High Fidelity?"

Contact Information

Mark L. Stone
6240 Hidden Woods Ct. #32
Springfield, VA 22152-2349
571 278 6332 cell

mark "at"marklstone "dot" com