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Journal articles on the topic 'Infinite-Dimensional linear programming'

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Published: 1 June 2024
Last updated: 31 July 2025

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1

Appa, Gautam, Edward J. Anderson, and Peter Nash. "Linear Programming in Infinite-Dimensional Spaces." Journal of the Operational Research Society 40, no. 1 (1989): 109. http://dx.doi.org/10.2307/2583085.

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2

Appa, Gautam. "Linear Programming in Infinite-Dimensional Spaces." Journal of the Operational Research Society 40, no. 1 (1989): 109–10. http://dx.doi.org/10.1057/jors.1989.13.

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3

Romeijn, H. Edwin, Robert L. Smith, and James C. Bean. "Duality in infinite dimensional linear programming." Mathematical Programming 53, no. 1-3 (1992): 79–97. http://dx.doi.org/10.1007/bf01585695.

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4

López, M. A. "Linear programming in infinite-dimensional spaces." European Journal of Operational Research 36, no. 1 (1988): 134–35. http://dx.doi.org/10.1016/0377-2217(88)90019-7.

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5

Romeijn, H. Edwin, and Robert L. Smith. "Shadow Prices in Infinite-Dimensional Linear Programming." Mathematics of Operations Research 23, no. 1 (1998): 239–56. http://dx.doi.org/10.1287/moor.23.1.239.

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6

Ho, Tvu-Ying, Yuung-Yih Lur, and Soon-Yi Wu. "The Difference between Finite Dimensional Linear Programming Problems and Infinite Dimensional Linear Programming Problems." Journal of Mathematical Analysis and Applications 207, no. 1 (1997): 192–205. http://dx.doi.org/10.1006/jmaa.1997.5279.

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7

Taksar, Michael I. "Infinite-Dimensional Linear Programming Approach to SingularStochastic Control." SIAM Journal on Control and Optimization 35, no. 2 (1997): 604–25. http://dx.doi.org/10.1137/s036301299528685x.

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8

Vinh, N. T., D. S. Kim, N. N. Tam, and N. D. Yen. "Duality gap function in infinite dimensional linear programming." Journal of Mathematical Analysis and Applications 437, no. 1 (2016): 1–15. http://dx.doi.org/10.1016/j.jmaa.2015.12.043.

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9

Balbas, Alejandro, and Antonio Heras. "Duality theory for infinite-dimensional multiobjective linear programming." European Journal of Operational Research 68, no. 3 (1993): 379–88. http://dx.doi.org/10.1016/0377-2217(93)90194-r.

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10

Kariotoglou, Nikolaos, Maryam Kamgarpour, Tyler H. Summers, and John Lygeros. "The Linear Programming Approach to Reach-Avoid Problems for Markov Decision Processes." Journal of Artificial Intelligence Research 60 (October 4, 2017): 263–85. http://dx.doi.org/10.1613/jair.5500.

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One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to maximize the probability of reaching a target set at a given time, while staying in a safe set at all prior times. We characterize the solution to this problem through an infinite dimensional linear program. We then develop a tractable approximation to the infinite dimensional linear program through finite dimensional approximations of the decisi
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11

Ito, Satoshi, Soon-Yi Wu, Ting-Jang Shiu, and Kok Lay Teo. "A numerical approach to infinite-dimensional linear programming in $L_1$ spaces." Journal of Industrial & Management Optimization 6, no. 1 (2010): 15–28. http://dx.doi.org/10.3934/jimo.2010.6.15.

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12

Mendiondo, Marta Susana, and Richard H. Stockbridge. "Approximation of Infinite-Dimensional Linear Programming Problems which Arise in Stochastic Control." SIAM Journal on Control and Optimization 36, no. 4 (1998): 1448–72. http://dx.doi.org/10.1137/s0363012996313367.

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13

ERIKSSON, BJORN, and MARTIJN PISTORIUS. "METHOD OF MOMENTS APPROACH TO PRICING DOUBLE BARRIER CONTRACTS IN POLYNOMIAL JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 14, no. 07 (2011): 1139–58. http://dx.doi.org/10.1142/s0219024911006644.

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We present a method of moments approach to pricing double barrier contracts when the underlying is modelled by a polynomial jump-diffusion. By general principles the price is linked to certain infinite dimensional linear programming problems. Subsequently approximating these by finite dimensional linear programming problems, upper and lower bounds for the prices of such options are found. We derive theoretical convergence results for this algorithm, and provide numerical illustrations by applying the method to the valuation of several double barrier-type contracts (double barrier knock-out cal
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14

Mulvey, J. M. "Infinite programming: Proceedings of an international symposium on infinite dimensional linear programming, Churchill College, Cambridge, United Kingdom, September 7–10, 1984." European Journal of Operational Research 27, no. 2 (1986): 259. http://dx.doi.org/10.1016/0377-2217(86)90077-9.

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15

Khanh, Pham Duy, Tran Hong Mo, and Trinh T. T. Tran. "Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems." Numerical Functional Analysis and Optimization 40, no. 8 (2019): 924–43. http://dx.doi.org/10.1080/01630563.2019.1566244.

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16

Levin, V. L. "On generic uniqueness of optimal solution in an infinite dimensional linear programming problem." Doklady Mathematics 78, no. 1 (2008): 490–92. http://dx.doi.org/10.1134/s1064562408040054.

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17

Nordebo, S., and Z. Zang. "Application of infinite dimensional linear programming to IIR filter design with time domain constraints." IEEE Transactions on Signal Processing 47, no. 7 (1999): 2060–63. http://dx.doi.org/10.1109/78.771057.

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18

Staffans, Olof J. "The Four-Block Model Matching Problem in $l^1 $ and Infinite-Dimensional Linear Programming." SIAM Journal on Control and Optimization 31, no. 3 (1993): 747–79. http://dx.doi.org/10.1137/0331034.

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19

Klabjan, Diego, and Daniel Adelman. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces." Mathematics of Operations Research 32, no. 3 (2007): 528–50. http://dx.doi.org/10.1287/moor.1070.0252.

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20

Bartl, David. "Farkas' Lemma, other theorems of the alternative, and linear programming in infinite-dimensional spaces: a purely linear-algebraic approach." Linear and Multilinear Algebra 55, no. 4 (2007): 327–53. http://dx.doi.org/10.1080/03081080600967820.

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21

Fang, Zheng, Andres Santos, Azeem M. Shaikh, and Alexander Torgovitsky. "Inference for Large‐Scale Linear Systems With Known Coefficients." Econometrica 91, no. 1 (2023): 299–327. http://dx.doi.org/10.3982/ecta18979.

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This paper considers the problem of testing whether there exists a non‐negative solution to a possibly under‐determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of identified parameters satisfying an infinite set of inequality restrictions. Using this characterization, we devise a test
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22

Boucekkine, Raouf, Giorgio Fabbri, Salvatore Federico, and Fausto Gozzi. "Geographic environmental Kuznets curves: the optimal growth linear-quadratic case." Mathematical Modelling of Natural Phenomena 14, no. 1 (2019): 105. http://dx.doi.org/10.1051/mmnp/2018076.

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We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asympt
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23

Friedland, Shmuel, Jingtong Ge, and Lihong Zhi. "Quantum Strassen’s theorem." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 03 (2020): 2050020. http://dx.doi.org/10.1142/s0219025720500204.

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Strassen’s theorem circa 1965 gives necessary and sufficient conditions on the existence of a probability measure on two product spaces with given support and two marginals. In the case where each product space is finite, Strassen’s theorem is reduced to a linear programming problem which can be solved using flow theory. A density matrix of bipartite quantum system is a quantum analog of a probability matrix on two finite product spaces. Partial traces of the density matrix are analogs of marginals. The support of the density matrix is its range. The analog of Strassen’s theorem in this case c
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24

Glimm, Tilmann, and Nick Henscheid. "Iterative Scheme for Solving Optimal Transportation Problems Arising in Reflector Design." ISRN Applied Mathematics 2013 (November 24, 2013): 1–12. http://dx.doi.org/10.1155/2013/635263.

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We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it has been shown previously that this problem is equivalent to an infinite-dimensional linear programming (LP) problem. Here we investigate techniques for constructing the two reflectors numerically by considering the finite-dimensional LP problems which arise as approximations to the infinite-dimensional problem. A straightforward discretization has the disa
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25

Pattnaik, Monalisha. "Optimality test in fuzzy inventory model for restricted budget and space: Move forward to a non-linear programming approach." Yugoslav Journal of Operations Research 25, no. 3 (2015): 457–70. http://dx.doi.org/10.2298/yjor130517023p.

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In this paper, the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ) model for restricted budget and space. Since various types of uncertainties and imprecision are inherent in real inventory problems, they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by the usual probabilistic models. The questions are how to define inventory optimization tasks in such environment and how to interpret the optimal solutions. This paper allow the modification of
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26

Rusmevichientong, Paat, Mika Sumida, and Huseyin Topaloglu. "Dynamic Assortment Optimization for Reusable Products with Random Usage Durations." Management Science 66, no. 7 (2020): 2820–44. http://dx.doi.org/10.1287/mnsc.2019.3346.

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We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and returns the product back to the firm to be used by other customers. The goal is to find a policy for deciding on the assortment to offer to each customer so that the total expected revenue over a finite selling horizon is maximized. The dynamic-programming formulation of this problem requires a high-dimensional state variable that keeps track of the on-hand product inventories, as well as the products
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27

Larysa, Koriashkina, та Dziuba Serhii. "МАТЕМАТИЧНІ МОДЕЛІ ТА МЕТОДИ РОЗМІЩЕННЯ ОБ’ЄКТІВ І ЗОНУВАННЯ ТЕРИТОРІЙ В СИСТЕМАХ ЕКСТРЕНОЇ ЛОГІСТИКИ". System technologies 6, № 149 (2024): 107–22. http://dx.doi.org/10.34185/1562-9945-6-149-2023-09.

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The mathematical models for distribution processes related to organizing precautionary measures in the event of threats or occurrences of man-made emergencies are presented. The tasks include optimal zoning of territories with the fixing of zones by objects of social purpose for service provision. Provision is made for: the possibility of overlapping zones in case the nearest center cannot provide the service; optimal placement of a certain number of new cen-ters of emergency logistics systems with simultaneous redistribution of the load on all their structural elements; the selection of locat
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28

Malozemov, Vassili N., and Natalya A. Solovyeva. "MDM method for solving the general quadratic problem of mathematical diagnostics." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 10 (68), no. 3 (2023): 516–29. http://dx.doi.org/10.21638/spbu01.2023.306.

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The term mathematical diagnostics was introduced by V. F. Demyanov in the early 2000s. The simplest problem of mathematical diagnostics is to determine the relative position of a certain point p and the convex hull C of a finite number of given points in n-dimensional Euclidean space. Of interest is the answer to the following questions: does the point p belong to the set C or not? If p does not belong to C, then what is the distance from p to C? In general problem of mathematical diagnostics two convex hulls are considered. The question is whether they have common points. If there are no comm
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29

Tovstik, Tatiana M. "Stationary reversibles processes MA and ARMA." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 10 (68), no. 3 (2023): 530–44. http://dx.doi.org/10.21638/spbu01.2023.307.

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The term mathematical diagnostics was introduced by V. F. Demyanov in the early 2000s. The simplest problem of mathematical diagnostics is to determine the relative position of a certain point p and the convex hull C of a finite number of given points in n-dimensional Euclidean space. Of interest is the answer to the following questions: does the point p belong to the set C or not? If p does not belong to C, then what is the distance from p to C? In general problem of mathematical diagnostics two convex hulls are considered. The question is whether they have common points. If there are no comm
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30

Kamgarpour, Maryam, and Tyler Summers. "On infinite dimensional linear programming approach to stochastic control * *This research is partially supported by M. Kamgarpour’s European Union ERC Starting Grant, CONENE and by T. Summers’ the US National Science Foundation under grant CNS-1566127." IFAC-PapersOnLine 50, no. 1 (2017): 6148–53. http://dx.doi.org/10.1016/j.ifacol.2017.08.979.

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31

Alzalg, Baha. "Barrier methods based on Jordan-Hilbert algebras for stochastic optimization in spin factors." RAIRO - Operations Research, December 22, 2023. http://dx.doi.org/10.1051/ro/2023198.

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Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration
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32

Leyffer, Sven, and Paul Manns. "Sequential linear integer programming for integer optimal control with total variation regularization." ESAIM: Control, Optimisation and Calculus of Variations, September 20, 2022. http://dx.doi.org/10.1051/cocv/2022059.

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We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minmizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonst
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33

Zălinescu, Constantin. "On the duality gap and Gale's example in infinite-dimensional conic linear programming." Journal of Mathematical Analysis and Applications, November 2022, 126868. http://dx.doi.org/10.1016/j.jmaa.2022.126868.

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34

Rahaman, Mijanur, Mohd Ishtyak, Iqbal Ahmad, and Rais Ahmad. "Split monotone variational inclusion problem involving Cayley operators." Georgian Mathematical Journal, September 30, 2022. http://dx.doi.org/10.1515/gmj-2022-2187.

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Abstract In this article, we introduce a new kind of split monotone variational inclusion problem involving Cayley operator in the setting of infinite-dimensional Hilbert spaces. We develop a general iterative method to approximate the solution of the split monotone variational inclusion problem involving Cayley operator. Under some suitable conditions, a convergence theorem for the sequences generated by the proposed iterative scheme is established, which also solves certain variational inequality problems related to strongly positive linear operators. Finally, a numerical example is presente
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35

Milz, Johannes. "Sample average approximations of strongly convex stochastic programs in Hilbert spaces." Optimization Letters, May 28, 2022. http://dx.doi.org/10.1007/s11590-022-01888-4.

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AbstractWe analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex with the same convexity parameter for each realization. Combined with a standard condition from the literature on stochastic programming, we establish non-asymptotic exponential tail bounds for the distance between the SAA solutions and the stochastic program’s solution, without assuming compactness of the feasible set. Our assumptions are verified on a class of infinite-dimensional optimization problems gover
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36

Yu, Huizhen. "On Linear Programming for Constrained and Unconstrained Average-Cost Markov Decision Processes with Countable Action Spaces and Strictly Unbounded Costs." Mathematics of Operations Research, December 15, 2021. http://dx.doi.org/10.1287/moor.2021.1177.

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We consider the linear programming approach for constrained and unconstrained Markov decision processes (MDPs) under the long-run average-cost criterion, where the class of MDPs in our study have Borel state spaces and discrete countable action spaces. Under a strict unboundedness condition on the one-stage costs and a recently introduced majorization condition on the state transition stochastic kernel, we study infinite-dimensional linear programs for the average-cost MDPs and prove the absence of a duality gap and other optimality results. Our results do not require a lower-semicontinuous MD
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37

Cardoen, Clément, Swann Marx, Anthony Nouy, and Nicolas Seguin. "A moment approach for entropy solutions of parameter-dependent hyperbolic conservation laws." Numerische Mathematik, July 15, 2024. http://dx.doi.org/10.1007/s00211-024-01428-5.

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AbstractWe propose a numerical method to solve parameter-dependent scalar hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020). This approach relies on a very weak notion of solution of nonlinear equations, namely parametric entropy measure-valued (MV) solutions, satisfying linear equations in the space of Borel measures. The infinite-dimensional linear problem is approximated by a hierarchy of convex, finite-dimensional, semidefinite programming problems, called Lasserre’s hierarchy. This gives us a sequence of approximation
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38

Narciso, Diogo A. C., and Efstratios N. Pistikopoulos. "Novel solution strategies for multiparametric nonlinear optimization problems with convex objective function and linear constraints." Optimization and Engineering, April 22, 2024. http://dx.doi.org/10.1007/s11081-024-09888-2.

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AbstractThis paper expands the multiparametric quadratic programming (mp-QP) framework presented in Narciso et al. (Comput Chem Eng 164:107882, 2022. https://doi.org/10.1016/j.compchemeng.2022.107882) to the more general multiparametric nonlinear programming (mp-NLP) case. First, the vector of parameters in mp-NLP problems is recast so that a unique transformed parameter is implicitly assigned to each of the inequality constraints. Maps of critical regions in this transformed space of parameters feature a set of 1-dimensional parametric edges (two per inequality constraint), which then greatly
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39

Lim, Tongseok, and Robert J. McCann. "Geometrical Bounds for Variance and Recentered Moments." Mathematics of Operations Research, May 24, 2021. http://dx.doi.org/10.1287/moor.2021.1125.

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We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu and of Bhatia and Davis concerning measures on the line to several dimensions. This is done using convex duality and (infinite-dimensional) linear programming. The following consequence of our bounds exhibits symmetry breaking, provides a new proof of Jung’s theorem, and turns out to have applications to the aggregation dynamics modelling attractive–repulsive interactions: among probability measures on [Formula: see text] whose support has diameter at m
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40

Zhang, Shixuan, and Xu Andy Sun. "Stochastic dual dynamic programming for multistage stochastic mixed-integer nonlinear optimization." Mathematical Programming, August 20, 2022. http://dx.doi.org/10.1007/s10107-022-01875-8.

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AbstractIn this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with non-Lipschitzian value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient is a new type of cuts based on generalized conjugacy. Several interesting classes of MS-MINLP are identified, where the new
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41

Brustle, Johannes, Sebastian Perez-Salazar, and Victor Verdugo. "Splitting Guarantees for Prophet Inequalities via Nonlinear Systems." Mathematics of Operations Research, April 17, 2025. https://doi.org/10.1287/moor.2024.0413.

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The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. k-selection prophet inequality problem, we sequentially observe n nonnegative random values sampled from a known distribution. Each time, a decision is made to accept or reject the value, and under the constraint of accepting at most k items. For k = 1, Hill and Kertz [Ann. Probab. 1982] provided an upper bound on the worst-case approximation ratio that was later matched by an algorithm of Correa et al. [Math.
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42

Fan, Xiangyi, and Grani A. Hanasusanto. "A Decision Rule Approach for Two-Stage Data-Driven Distributionally Robust Optimization Problems with Random Recourse." INFORMS Journal on Computing, November 29, 2023. http://dx.doi.org/10.1287/ijoc.2021.0306.

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We study two-stage stochastic optimization problems with random recourse, where the coefficients of the adaptive decisions involve uncertain parameters. To deal with the infinite-dimensional recourse decisions, we propose a scalable approximation scheme via piecewise linear and piecewise quadratic decision rules. We develop a data-driven distributionally robust framework with two layers of robustness to address distributional uncertainty. We also establish out-of-sample performance guarantees for the proposed scheme. Applying known ideas, the resulting optimization problem can be reformulated
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