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- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- Math. Program.
- 2011

An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981,â€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- Math. Program.
- 2011

An Adaptive Regularisation framework using Cubics (ARC) was proposed for unconstrained optimization and analysed in Cartis, Gould and Toint (Part I, Math Program, doi:10.1007/s10107-009-0286-5,â€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- SIAM Journal on Optimization
- 2010

It is shown that the steepest descent and Newtonâ€™s method for unconstrained nonconvex optimization under standard assumptions may be both require a number of iterations and function evaluationsâ€¦ (More)

- Jeffrey D. Blanchard, Coralia Cartis, Jared Tanner
- SIAM Review
- 2011

Compressed sensing (CS) seeks to recover an unknown vector with N entries by making far fewer than N measurements; it posits that the number of CS measurements should be comparable to the informationâ€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- SIAM Journal on Optimization
- 2011

We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it isâ€¦ (More)

An Adaptive Cubic Overestimation (ACO) algorithm for unconstrained optimization, generalizing a method due to Nesterov & Polyak (Math. Programming 108, 2006, pp 177-205), is proposed. At eachâ€¦ (More)

Consider a measurement matrix A of size nÃ—N , with n < N , y a signal in RN , and b = Ay the observed measurement of the vector y. From knowledge of (b, A), compressed sensing seeks to recover theâ€¦ (More)

The adaptive cubic regularization algorithm described in Cartis, Gould and Toint (2009, 2010) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over aâ€¦ (More)

- Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
- J. Complexity
- 2012

This paper examines worst-case evaluation bounds for finding weak minimizers in unconstrained optimization. For the cubic regularization algorithm, Nesterov and Polyak (2006) [15] and Cartis et al.â€¦ (More)

We consider a general class of second-order iterations for unconstrained optimization that includes regularization and trust-region variants of Newtonâ€™s method. For each method in this class, weâ€¦ (More)