Society for Industrial and Applied Mathematics (June 10, 2009)

This textbook provides undergraduate students with an introduction to optimization and its uses for relevant and realistic problems. The only prerequisite for readers is a basic understanding of multivariable calculus because additional materials, such as explanations of matrix tools, are provided in a series of Asides both throughout the text at relevant points and in a handy appendix.

Springer Briefs in Optimization. Springer, New York, 2012

This monograph presents and analyzes a unifying framework for a wide variety of numerical minimization methods. Our “reduce-or-retreat” framework is a conceptual method outline that covers essentially any method whose iterations choose between the two options of reducing the objective in some way at a trial point, or (if reduction is not possible) retreating to a closer set of trial points. Included in this category are many derivative-based methods (which depend on the objective gradient to generate trial points), as well as many derivative-free and direct methods that generate trial points either from some model of the objective or from some designated pattern in the variable space.

- Hull-Volume with applications to convergence analysis in
*Journal of Optimization Theory* and Applications **153** (2012), no. 3, 1--17.
- Constraint Incorporation in Optimization in
*Mathematical Programming, Series A* **110** (2007), no. 3, 615--639.
- Supercalm multifunctions for convergence analysis in
*Set-Valued Anal.* **14** (2006), no. 3, 249--261.
- Convergence of successive approximation methods with parameter target sets in
*Math. Oper. Res.* **30**(2005), no. 3, 765--784.
- A generic algorithm for solving inclusions in
*SIAM Journal on Optimization* **15** (2005), 430--455.
- Coderivatives in parametric optimization (with Boris S. Mordukhovich) in
*Math. Program., Ser. A* **99**(2004), 311--327

- Stationarity and convergence in reduce-or-retreat minimization. Springer Briefs in Optimization.
*Springer, New York,* 2012.
- Hull-Volume with applications to convergence analysis in
*Journal of Optimization Theory and Applications* **153** (2012), no. 3, 633--649.
- Constraint Incorporation in Optimization in
*Mathematical Programming, Series A* **110** (2007), no. 3, 615--639.
- Supercalm multifunctions for convergence analysis in
*Set-Valued Anal.* **14** (2006), no. 3, 249--261.
- Convergence of successive approximation methods with parameter target sets in
*Math. Oper. Res.* **30**(2005), no. 3, 765--784.
- A generic algorithm for solving inclusions in
*SIAM Journal on Optimization* **15** (2005), 430--455.
- Coderivatives in parametric optimization (with Boris S. Mordukhovich) in
*Math. Program., Ser. A* **99**(2004), 311--327
- Scaled stability in variational problems in
*SIAM Journal on Optimization.* **12** (2002), 861--874.
- Solution sensitivity from general principles in
*SIAM Journal on Control and Optimization,* **40** (2001), 1--38.
- Second-order epi-derivatives of composite functionals in
*Annals of Operations Research,* **101** (2001), 267--281.
- Lipschitzian multifunctions and a Lipschitzian inverse mapping theorem in
*Mathematics of Operations Research,* **26** (2001), 105--118.
- Calm minima in parameterized finite-dimensional optimization in
*SIAM Journal on Optimization,* **11**(2000), 160--178.
- Stability of locally optimal solutions (with R. Poliquin and R.T. Rockafellar) in
*SIAM Journal on Optimization,* **10** (2000), 580-604.
- Sensitivity of solutions to variational inequalities on Banach spaces in
*SIAM Journal on Control and Optimization,* **38** (1999), 50-60.
- Nonsingularity conditions for multifunctions in
*Set-Valued Analysis,* **7** (1999), 89-99.
- Stability of solutions to parameterized nonlinear complementarity problems in
*Mathematical Programming,* **85** (1999), 397-406.
- Convex composite functions in Banach spaces and the primal lower-nice property (with C. Combari, A. Elhilali Alaoui, R. Poliquin, and L. Thibault) in
*Proceedings of the American Mathematical Society* , **126**(1998), 3701-3708.
- Characterizing the single-valuedness of multifunctions (with R. Poliquin) in
*Set-vlaued Analysis,* **5**(1997), 351-364.
- Implicit multifunction theorems for the sensitivity analysis of variational conditions in
*Mathematical Programming* , **74** (1996), 333-350. *Errata*
- Proto-derivatives and the geometry of solution mappings in nonlinear programming (with R. T. Rockafellar) in
*Nonlinear Optimization and Applications* , pages 343-365. Plenum, 1996.
- Variational conditions and the proto-differentiation of partial subgradient mappings (with R. T. Rockafellar) in
*Nonlinear Analysis, Theory, Methods, and Applications* , **26** (1995), 1951-1964.
- Sensitivity of solutions in nonlinear programming problems with nonunique multipliers (with R. T. Rockafellar), in D.-Z. Du, L. Qi, and R.S. Womersley, editors,
*Recent Advances in Nonsmooth Optimization* , pages 215-223. World Scientific, 1995.
- Partial extensions of Attouch's theorem with application to proto-differentiability of subgradient mappings (with R. Poliquin and L. Thibault) in
*Transactions of the American Mathematical Society* , **347** (1995), 1269-1294.
- Sensitivity analysis of solutions to generalized equations (with R. T. Rockafellar) in
*Transactions of the American Mathematical Society* , **345** (1994), 661-671.
- Second-order epi-derivatives of integral functionals in
*Set-Valued Analysis* , **1** (1993), 379-392.

MathSciNet reviews for most of the above »