Necessary Conditions for an Extremum

Pshenichnyi, B. N.

doi:10.1201/9781003064848

Cited by 22 publications

(17 citation statements)

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“…Dutta and Lalitha [9] generalize the previous result to the case where C is represented by locally Lipschitz functions, not necessarily differentiable nor convex, but regular in the sense of Clarke [10] (see also Definition 2). Martínez-Legaz [11] further generalize the result to the case where C is represented by tangentially convex functions [12,13]. Kabgani et al [14] generalize the result to the case where C is represented by functions that admit an upper regular convexificator URC [15] (see also Definition 3).…”

Section: Example 1 Consider the Convex Feasible Region Given Bymentioning

confidence: 89%

On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm

2020

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Recently, Kronqvist et al. (J Global Optim 64(2):249–272, 2016) rediscovered the supporting hyperplane algorithm of Veinott (Oper Res 15(1):147–152, 1967) and demonstrated its computational benefits for solving convex mixed integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm (J Soc Ind Appl Math 8(4):703–712, 1960) applied to a particular reformulation of the problem. As a result, we extend the applicability of the supporting hyperplane algorithm to convex problems represented by a class of general, not necessarily convex nor differentiable, functions.

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Section: Example 1 Consider the Convex Feasible Region Given Bymentioning

confidence: 89%

On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm

2020

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“…The constrained optimization problem (3.2) is equivalent to the unconstrained optimization problem (see book by Pshenichnyj [34])…”

Section: Minimax-robust Methods Of Filteringmentioning

confidence: 99%

“…This condition makes it possible to find the least favourable spectral densities in some special classes of spectral densities D (see books by Ioffe and Tihomirov [35], Pshenichnyj [34], Rockafellar [36]). Note, that the form of the functional ∆(h(F 0 , G 0 ); F, G) is convenient for application of the Lagrange method of indefinite multipliers for finding solution of the problem (3.2).…”

Section: Minimax-robust Methods Of Filteringmentioning

confidence: 99%

Filtering of Multidimensional Stationary Processes with Missing Observations

Masyutka

Moklyachuk

Sidei

2019

Universal Journal of Mathematics and Applications

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The problem of the mean-square optimal linear estimation of the functional Aξ = R s a(t)ξ(−t)dt, which depends on the unknown values of stochastic stationary process ξ(t) from observations of the process ξ(t) +Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functional are proposed under the condition of spectral certainty, where spectral densities of the processes ξ(t) and η(t) are exactly known. The minimax (robust) method of estimation is applied in the case where spectral densities are not known exactly, but sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics are proposed for some special sets of admissible densities.

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“…As a consequence a wide portion of the literature is devoted to the analysis of the costate vector and some qualification conditions have been established in order to ensure that it has no singular component (see, e.g., [14,47,50,55]). Note that the related theme of state constrained discrete-time optimal control problems has also been investigated in the literature (see, e.g., [30,62]).…”

Section: State Constrained Optimal Control Problemsmentioning

confidence: 99%

Pontryagin maximum principle for state constrained optimal sampled-data control problems on time scales

Bettiol

Bourdin

2021

ESAIM: COCV

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In this paper we consider optimal sampled-data control problems on time scales with inequality state constraints. A Pontryagin maximum principle is established, extending to the state constrained case existing results in the time scale literature. The proof is based on the Ekeland variational principle and on the concept of implicit spike variations adapted to the time scale setting. The main result is then applied to continuous-time min-max optimal sampled-data control problems and a maximal velocity minimization problem for the harmonic oscillator with sampled-data control is numerically solved for illustration.

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Necessary Conditions for an Extremum

Cited by 22 publications

References 0 publications

On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm

On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm

Filtering of Multidimensional Stationary Processes with Missing Observations

Pontryagin maximum principle for state constrained optimal sampled-data control problems on time scales

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