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- Aharon Ben-Tal, Arkadi Nemirovski
- Math. Oper. Res.
- 1998

We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main… (More)

- Aharon Ben-Tal, Arkadi Nemirovski
- Oper. Res. Lett.
- 1999

We treat in this paper Linear Programming (LP) problems with uncertain data. The focus is on uncertainty associated with hard constraints: those which must be satisfied, whatever is the actual realization of the data (within a prescribed uncertainty set). We suggest a modeling methodology whereas an uncertain LP is replaced by its Robust Counterpart (RC).… (More)

- Aharon Ben-Tal, Laurent El Ghaoui, +14 authors ROBook May
- 2004

We propose new methodologies in robust optimization that promise greater tractability, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second order… (More)

- Aharon Ben-Tal, A. Goryashko, E. Guslitzer, Arkadi Nemirovski
- Math. Program.
- 2004

We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”non-adjustable variables”), while the other part are variables that can be chosen after the realization (”adjustable variables”). We extend the Robust… (More)

- Aharon Ben-Tal, Arkadi Nemirovski
- Math. Program.
- 2000

Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1-3]; El Ghaoui et al. [5,6]) to produce “robust” solutions of the above… (More)

- Aharon Ben-Tal, Arkadi Nemirovski
- Math. Program.
- 2002

Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and semidefinite programming. For these cases, computationally… (More)

- Aharon Ben-Tal, Arkadi Nemirovski
- SIAM Journal on Optimization
- 1997

We present and motivate a new model of the truss topology design problem, where the rigidity of the resulting truss with respect both to given loading scenarios and small “occasional” loads is optimized. It is shown that the resulting optimization problem is a semidefinite program. We derive and analyze several equivalent reformulations of the problem and… (More)

- Amir Beck, Aharon Ben-Tal, Luba Tetruashvili
- J. Global Optimization
- 2010

We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions. Under appropriate conditions on this upper bounding convex function, a monotone convergence to a KKT… (More)

- Aharon Ben-Tal, Arkadi Nemirovski
- Math. Oper. Res.
- 2001

We demonstrate that a conic quadratic problem min x { ex ∣Ax ≥ b, ‖A`x− b`‖2 ≤ c` x− d`, ` = 1, ...,m } , ‖y‖2 = √ yT y, (CQP) is “polynomially reducible” to Linear Programming. We demonstrate this by constructing, for every ∈ (0, 12 ], an LP program (explicitly given in terms of and the data of (CQP)) min x,u { ex ∣P ( x u ) + p ≥ 0 } (LP) with the… (More)