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- Kamil A. Khan, Paul I. Barton
- Optimization Methods and Software
- 2015

Numerical methods for non-smooth equation-solving and optimization often require generalized derivative information in the form of elements of the Clarke Jacobian or the B-subdifferential. It is… (More)

- Kamil A. Khan, Paul I. Barton
- ACM Trans. Math. Softw.
- 2013

Bundle methods for nonsmooth optimization and semismooth Newton methods for nonsmooth equation solving both require computation of elements of the (Clarke) generalized Jacobian, which provides slope… (More)

- Kamil A. Khan, Paul I. Barton
- J. Optimization Theory and Applications
- 2014

Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic… (More)

- Kamil A. Khan, Paul I. Barton
- 53rd IEEE Conference on Decision and Control
- 2014

Recent advances in nonsmooth sensitivity analysis are extended to describe particular elements of Clarke's generalized gradient for the nonsmooth objective function of a nonsmooth optimal control… (More)

- Kamil A. Khan, Jeffrey Larson, Stefan M. Wild
- SIAM Journal on Optimization
- 2018

We develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \triangleq \psi + h \circ F$ when $\psi$ is smooth with known derivatives, $h$ is a known, nonsmoo...

- Kamil A. Khan, Harry A. J. Watson, Paul I. Barton
- J. Global Optimization
- 2016

McCormick’s classical relaxation technique constructs closed-form convex and concave relaxations of compositions of simple intrinsic functions. These relaxations have several properties which make… (More)

- Kamil A. Khan, Paul I. Barton
- IEEE Transactions on Automatic Control
- 2017

Established sensitivity results for hybrid discrete/continuous dynamic systems are generalized by relaxing smoothness assumptions on the functions governing the systems' continuous evolution and… (More)

- Kamil A. Khan, Vibhu P. Saxena, Paul I. Barton
- SIAM J. Scientific Computing
- 2011

A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics… (More)

- Kamil A. Khan
- Optimization Methods and Software
- 2018

A recent nonsmooth vector forward mode of algorithmic differentiation (AD) computes Nesterov's L-derivatives for nonsmooth composite functions; these L-derivatives provide useful sensitivity… (More)

- Jose A. Gomez, Kai Höffner, Kamil A. Khan, Paul I. Barton
- J. Optimization Theory and Applications
- 2018

Lexicographic linear programs are fixed-priority multiobjective linear programs that are a useful model of biological systems using flux balance analysis and for goal-programming problems. The… (More)