An Incremental Method for Solving Convex Finite Min-Max Problems

Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna

doi:10.1287/moor.1050.0175

Cited by 42 publications

(53 citation statements)

References 10 publications

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“…This is time-consuming if the number of the component functions is large. In order to reduce the number of component function evaluations, Gaudioso et al [6] proposed that at each point y l just evaluate one of the component functions, say f j l (y l ), for some j l ∈ J, along with a subgradient g…”

Section: An Improved Partial Bundle Methods For Linearly Constrained Mmentioning

confidence: 99%

“…(i) Our method not only extends the method of [6] to linearly constrained case, but also improves the descent test criterion used in [6] and [9] (see Remark 1 for details).…”

mentioning

confidence: 94%

“…In what follows, we particularly concern the case where the component functions are not necessarily differentiable. In order to reduce the number of component function evaluations, Gaudioso et al [6] proposed an incremental bundle method for solving convex unconstrained minimax problems, in which a partial cutting-planes model of the objective function f is introduced. Hare & Macklem [7] and Hare & Nutini [8] proposed a derivativefree gradient sampling method for solving unconstrained minimax problems by applying the gradient sampling idea of Burke et al [4].…”

mentioning

confidence: 99%

“…Liuzzi et al [18] presented a derivative-free method for linearly constrained minimax problems by using a smoothing technique based on an exponential penalty function. Jian et al [9] proposed a feasible descent bundle method for general inequality constrained minimax problems by using the partial cutting-planes model of [6]. Tang et al [22] proposed a proximal-projection partial bundle method for convex constrained minimax problems by combining the partial cutting-planes model of [6] with the proximal-projection idea of [13,15].…”

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confidence: 99%

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An improved partial bundle method for linearly constrained minimax problems

Tang

Chen

Jian

2016

Stat., optim. inf. comput.

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In this paper, we propose an improved partial bundle method for solving linearly constrained minimax problems. In order to reduce the number of component function evaluations, we utilize a partial cutting-planes model to substitute for the traditional one. At each iteration, only one quadratic programming subproblem needs to be solved to obtain a new trial point. An improved descent test criterion is introduced to simplify the algorithm. The method produces a sequence of feasible trial points, and ensures that the objective function is monotonically decreasing on the sequence of stability centers. Global convergence of the algorithm is established. Moreover, we utilize the subgradient aggregation strategy to control the size of the bundle and therefore overcome the difficulty of computation and storage. Finally, some preliminary numerical results show that the proposed method is effective.

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Section: An Improved Partial Bundle Methods For Linearly Constrained Mmentioning

confidence: 99%

“…(i) Our method not only extends the method of [6] to linearly constrained case, but also improves the descent test criterion used in [6] and [9] (see Remark 1 for details).…”

mentioning

confidence: 94%

mentioning

confidence: 99%

mentioning

confidence: 99%

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An improved partial bundle method for linearly constrained minimax problems

Tang

Chen

Jian

2016

Stat., optim. inf. comput.

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“…The incremental idea have been extended to min-max problems through the use of bundle methods by Gaudioso, Giallombardo, and Miglionico [11]. The presence of noise in incremental subgradient methods was addressed by Solodov and Zavriev in [26] for a compact constraint set X and the diminishing stepsize rule.…”

Section: Implications For Incremental K -Subgradient Methodsmentioning

confidence: 99%

The effect of deterministic noise in subgradient methods

Nedić

Bertsekas

2009

Math. Program.

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In this paper, we study the influence of noise on subgradient methods for convex constrained optimization. The noise may be due to various sources, and is manifested in inexact computation of the subgradients and function values. Assuming that the noise is deterministic and bounded, we discuss the convergence properties for two cases: the case where the constraint set is compact, and the case where this set need not be compact but the objective function has a sharp set of minima (for example the function is polyhedral). In both cases, using several different stepsize rules, we prove convergence to the optimal value within some tolerance that is given explicitly in terms of the errors. In the first case, the tolerance is nonzero, but in the second case, the optimal value can be obtained exactly, provided the size of the error in the subgradient computation is below some threshold. We then extend these results to objective functions that are the sum of a large number of convex functions, in which case an incremental subgradient method can be used.

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Chance-Constrained Programming

2013

Encyclopedia of Operations Research and Management Science

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In a way the basis for this thesis was laid in 2005 when together with some colleagues we were quantifying the impact of uncertainty on weekly unit-commitment. A fruitful collaboration with Pierre Thomas and Riadh Zorgati led to the birth of a software package called LEA ("Laboratoire des Expérimentations des Aléas") in the same year. From a technical perspective this software package allowed the user to execute a simple multiscenario approach around a deterministic optimization kernel. The innovating part was set up with Bernard Beauzamy. Instead of drawing scenarios as iid samples from some law (or black box software), the idea was to build artificial englobing scenarios allowing for bounding of output with only little computational effort. These experiments led, only much later, to an industrial software package. In any case this is how together with Riadh Zorgati, I got interested in dealing with uncertainty in an appropriate way. We had many discussions on Scenario generation, Robust Optimization etc These discussions were also greatly nourished by discussions with Michel Minoux. Around the same time, we had the chance to meet René Henrion and attend a seminar he gave. Chance constrained programming looked like a very powerful and intuitive way to deal with uncertainty. With good hopes and enthusiasm we set out to look where uncertainty in Energy Management plays a key role and should be dealt with appropriately. Once these structures identified we started experimenting with safe tractable approximations of chance constraints, scenario type of approaches and also Robust Optimization. Somewhere in 2009 we had to chance to work closely together with René Henrion and look to what extent Chance Constrained programming could be applied in Energy Management. This led me to be greatly intrigued by this field, and ultimately, gave me a desire to deeply understand this domain. Thanks to EDF I have had the opportunity to do this Thesis in part time. I hope to have contributed to the domain and continue to do so in the future. I do firmly believe that Chance Constrained Programming will be important in Energy Management in the near future.Thanking people after 10 years of work at EDF is almost a dangerous undertaking since we are bound to forget someone with whom we have had interesting discussions. Nonetheless I will make this attempt at my own risks.First of all I would like to thank Riadh Zorgati, who is a good friend and colleague. We share many views and in particular that (fundamental) research should have its place in an(y) industrial company. I would also like to thank Grace Doukopoulos, Olivier Feron, Nadia Oudjane, Cyrille Strugarek and Xavier Warin for the many interesting discussions (and years of joint work). Thanks to Thomas Triboulet, Laurent Mulot and their pragmatic viewpoint of what at EDF we commonly call "le métier" it is possible to obtain a partial view of the underlying structures of the optimization problems at hand. This allows for important progress in identifying the key features of Energy Ma...

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An Incremental Method for Solving Convex Finite Min-Max Problems

Cited by 42 publications

References 10 publications

An improved partial bundle method for linearly constrained minimax problems

An improved partial bundle method for linearly constrained minimax problems

The effect of deterministic noise in subgradient methods

Chance-Constrained Programming

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