| 1. |
- Agram, Nacira, Associate professor, 1987-, et al.
(författare)
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Impulse Control of Conditional McKean–Vlasov Jump Diffusions
- 2024
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Nature. - 0022-3239 .- 1573-2878. ; 200:3, s. 1100-1130
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider impulse control problems involving conditional McKean–Vlasov jump diffusions, with the common noise coming from the σ-algebra generated by the first components of a Brownian motion and an independent compensated Poisson random measure. We first study the well-posedness of the conditional McKean–Vlasov stochastic differential equations (SDEs) with jumps. Then, we prove the associated Fokker–Planck stochastic partial differential equation (SPDE) with jumps. Next, we establish a verification theorem for impulse control problems involving conditional McKean–Vlasov jump diffusions. We obtain a Markovian system by combining the state equation with the associated Fokker–Planck SPDE for the conditional law of the state. Then we derive sufficient variational inequalities for a function to be the value function of the impulse control problem, and for an impulse control to be the optimal control. We illustrate our results by applying them to the study of an optimal stream of dividends under transaction costs. We obtain the solution explicitly by finding a function and an associated impulse control, which satisfy the verification theorem.
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| 2. |
- Agram, Nacira, 1987-, et al.
(författare)
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Malliavin calculus and optimal control of stochastic Volterra equations
- 2015
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Ingår i: Journal of Optimization Theory and Applications. - : Springer. - 0022-3239 .- 1573-2878. ; 167:3, s. 1070-1094
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Tidskriftsartikel (refereegranskat)abstract
- Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore, classical methods, such as dynamic programming, cannot be used to study optimal control problems for such equations. However, we show that using Malliavin calculus, it is possible to formulate modified functional types of maximum principle suitable for such systems. This principle also applies to situations where the controller has only partial information available to base her decisions upon. We present both a Mangasarian sufficient condition and a Pontryagin-type maximum principle of this type, and then, we use the results to study some specific examples. In particular, we solve an optimal portfolio problem in a financial market model with memory.
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| 3. |
- Axsäter, Sven
(författare)
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Extension of the extended basic period approach for economic lot scheduling problems
- 1987
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Ingår i: Journal of Optimization Theory and Applications. - 0022-3239 .- 1573-2878. ; 52:No 2, s. 179-189
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses the problem of choosing cyclical production patterns for several products which are produced on a common production facility. The extended basic period approach of Elmaghraby is extended by allowing more than two basic periods. The problem of dimensionality of the dynamic programming formulation is dealt with by aggregating the capacity data in different basic periods
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| 4. |
- Bielecki, Tomasz R., et al.
(författare)
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Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model
- 2014
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 161:1, s. 90-102
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Tidskriftsartikel (refereegranskat)abstract
- We devise a bottom-up dynamic model of portfolio credit risk where instantaneous contagion is represented by the possibility of simultaneous defaults. Due to a Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-step procedure, much like in a standard static copula setup. In this sense this solves the bottom-up top-down puzzle which the CDO industry had been trying to do for a long time. This model can be used for any dynamic portfolio credit risk issue, such as dynamic hedging of CDOs by CDSs, or CVA computations on credit portfolios.
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| 5. |
- Bouchard, B., et al.
(författare)
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Quenched Mass Transport of Particles Toward a Target
- 2020
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Ingår i: Journal of Optimization Theory and Applications. - : Springer. - 0022-3239 .- 1573-2878. ; 186:2, s. 345-374
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Tidskriftsartikel (refereegranskat)abstract
- We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability distributions, at a fixed time horizon. Here, laws are considered conditionally to the path of the Brownian motion that drives the system. This kind of problems is motivated by limiting behavior of interacting particles systems with applications in, for example, agricultural crop management. We establish a version of the geometric dynamic programming principle for the associated reachability sets and prove that the corresponding value function is a viscosity solution of a geometric partial differential equation. This provides a characterization of the initial masses that can be almost surely transported toward a given target, along the paths of a stochastic differential equation. Our results extend those of Soner and Touzi, Journal of the European Mathematical Society (2002) to our setting.
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| 6. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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A Dual Active-Set Algorithm for Regularized Monotonic Regression
- 2017
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Ingår i: Journal of Optimization Theory and Applications. - : Springer. - 0022-3239 .- 1573-2878. ; 172:3, s. 929-949
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Tidskriftsartikel (refereegranskat)abstract
- Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.
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| 7. |
- Carlsson, Marcus
(författare)
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On Convex Envelopes and Regularization of Non-convex Functionals Without Moving Global Minima
- 2019
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 183:1, s. 66-84
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Tidskriftsartikel (refereegranskat)abstract
- We provide theory for the computation of convex envelopes of non-convex functionals including an ℓ2-term and use these to suggest a method for regularizing a more general set of problems. The applications are particularly aimed at compressed sensing and low-rank recovery problems, but the theory relies on results which potentially could be useful also for other types of non-convex problems. For optimization problems where the ℓ2-term contains a singular matrix, we prove that the regularizations never move the global minima. This result in turn relies on a theorem concerning the structure of convex envelopes, which is interesting in its own right. It says that at any point where the convex envelope does not touch the non-convex functional, we necessarily have a direction in which the convex envelope is affine.
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| 8. |
- Cromvik, Christoffer, 1980, et al.
(författare)
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On the robustness of global optima and stationary solutions to stochastic mathematical programs with equilibrium constraints, Part II: Applications
- 2010
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 144:3, s. 479-500
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Tidskriftsartikel (refereegranskat)abstract
- In a companion paper (Cromvik and Patriksson, Part I, J. Optim. Theory Appl., 2010), the mathematical modeling framework SMPEC was studied; in particular, global optima and stationary solutions to SMPECs were shown to be robust with respect to the underlying probability distribution under certain assumptions. Further, the framework and theory were elaborated to cover extensions of the upper-level objective: minimization of the conditional value-at-risk (CVaR) and treatment of the multiobjective case. In this paper, we consider two applications of these results: a classic traffic network design problem, where travel costs are uncertain, and the optimization of a treatment plan in intensity modulated radiation therapy, where the machine parameters and the position of the organs are uncertain. Owing to the generality of SMPEC, we can model these two very different applications within the same framework. Our findings illustrate the large potential in utilizing the SMPEC formalism for modeling and analysis purposes; in particular, information from scenarios in the lower-level problem may provide very useful additional insights into a particular application.
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| 9. |
- Emamizadeh, Behrouz, et al.
(författare)
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An Elliptic Optimal Control Problem and its Two Relaxations
- 2017
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Ingår i: Journal of Optimization Theory and Applications. - New York, NY : Springer. - 0022-3239 .- 1573-2878. ; 172:2, s. 455-465
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Tidskriftsartikel (refereegranskat)abstract
- In this note, we consider a control theory problem involving a strictly convex energy functional, which is not Gâteaux differentiable. The functional came up in the study of a shape optimization problem, and here we focus on the minimization of this functional. We relax the problem in two different ways and show that the relaxed variants can be solved by applying some recent results on two-phase obstacle-like problems of free boundary type. We derive an important qualitative property of the solutions, i.e., we prove that the minimizers are three-valued, a result which significantly reduces the search space for the relevant numerical algorithms. © 2016, Springer Science+Business Media New York.
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| 10. |
- Eriksson, J, et al.
(författare)
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Regularization methods for uniformly rank-deficient nonlinear least-squares problems
- 2005
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 127:1, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In solving the nonlinear least-squares problem of minimizing ||f(x)||22, difficulties arise with standard approaches, such as the Levenberg-Marquardt approach, when the Jacobian of f is rank-deficient or very ill-conditioned at the solution. To handle this difficulty, we study a special class of least-squares problems that are uniformly rank-deficient, i.e., the Jacobian of f has the same deficient rank in the neighborhood of a solution. For such problems, the solution is not locally unique. We present two solution tecniques: (i) finding a minimum-norm solution to the basic problem, (ii) using a Tikhonov regularization. Optimality conditions and algorithms are given for both of these strategies. Asymptotical convergence properties of the algorithms are derived and confirmed by numerical experiments. Extensions of the presented ideas make it possible to solve more general nonlinear least-squares problems in which the Jacobian of f at the solution is rank-deficient or ill-conditioned.
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