Linear lexicographic optimization

Isermann, Heinz

doi:10.1007/bf01782758

Cited by 89 publications

(37 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We follow this procedure until we find a subset that contains a family of optimal solutions for sparsity levels k 1 , k 2 , k 3 , · · · . This approach is known as the lexicographic optimization method (see, e.g., [10] and [11]). …”

Section: Detector Performance and Lexicographic Optimizationmentioning

confidence: 99%

“…We use a lexicographic optimization (see, e.g., [9], [10], and [11]) approach to design the matrix Φ that maximizes the worst-case detection SNR, where the worst-case is with respect to the location of nonzero entries of θ and their values. This is a design for robustness with respect to the worst sparse signal that can be produced in the basis Ψ.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and grassmannian packings

Zahedi

Pezeshki

Chong

2010

Proceedings of the 2010 American Control Conference

View full text Add to dashboard Cite

Detecting a sparse signal in noise is fundamentally different from reconstructing a sparse signal, as the objective is to optimize a detection performance criterion rather than to find the sparsest signal that satisfies a linear observation equation. In this paper, we consider the design of lowdimensional (compressive) measurement matrices for detecting sparse signals in white Gaussian noise. We use a lexicographic optimization approach to maximize the worst-case signal-tonoise ratio (SNR). More specifically, we find an optimal solution for a k-sparse signal among optimal solutions subject to sparsity level k − 1. We show that for all sparse signals, columns of the optimal measurement matrix must form a uniform tight frame. For 2-sparse signals, the smallest angle among angles between element pairs of this frame must be maximized. In this case, the optimal solution matrix is an optimal Grassmannian packing. For k-sparse signals where k > 2, the largest angle among such angles must be as close to the maximum smallest angle as possible. We show that under certain conditions, columns of the optimal measurement matrix form an equiangular uniform tight frame. For this case, we derive an expression for the maximal SNR in the worst-case scenario, as a function of the signal dimension and the number of measurements.

show abstract

Section: Detector Performance and Lexicographic Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and grassmannian packings

Zahedi

Pezeshki

Chong

2010

Proceedings of the 2010 American Control Conference

View full text Add to dashboard Cite

show abstract

“…For other results concerning the linear lexicographic optimization problem, see Isermann H (1982); the nonlinear case has been studied recently by M. Lupt~ik and F. Turnovec (1990).…”

Section: ~ There Exists a Unitary Lower Triangular P • Matrix L Such mentioning

confidence: 98%

Characterizations of efficient solutions under polyhedrality assumptions

Martínez-Legaz

1991

ZOR - Methods and Models of Operations Research

View full text Add to dashboard Cite

Summary:We give several characterizations of efficient solutions of subsets of R p (with respect to compatible preorders) in terms of the lexicographical order, under the assumptions that the set of admissible points is a convex polyhedron or the nonnegative cone corresponding to the preorder is polyhedral. We also characterize the lexicographical minimum of a convex polyhedron by means of the componentwise order and unitary lower triangular matrices.

show abstract

“…where the optimal solutionw * ∈ satisfies w * lex ṽ ∀ṽ ∈ Although this may not be a standard mathematical programming problem, we can obtain the optimal solution by solving a sequence of optimization problems (see Isermann 1982, Ogryczak et al 2005 as follows:…”

Section: Lexicographic Min-max Fairnessmentioning

confidence: 99%

Mitigating Delays and Unfairness in Appointment Systems

2017

Management Science

View full text Add to dashboard Cite

W e consider an appointment system where heterogeneous participants are sequenced and scheduled for service. Because service times are uncertain, the aims are to mitigate the unpleasantness experienced by the participants in the system when their waiting times or delays exceed acceptable thresholds and to address fairness in the balancing of service levels among participants. To evaluate uncertain delays, we propose the Delay Unpleasantness Measure, which takes into account the frequency and intensity of delays above a threshold, and introduce the concept of lexicographic min-max fairness to design appointment systems from the perspective of the worst-off participants. We focus our study in the healthcare industry in balancing physicians' overtime and patients' waiting times in which patients are distinguished by their service time characterizations. The model can be adapted in the robust setting when the underlying probability distribution is not fully available. To capture the correlation between uncertain service times, we suggest using the mean absolute deviations as the descriptive statistics in the distributional uncertainty set to preserve the linearity of the model. The optimal sequencing and scheduling decisions can be derived by solving a sequence of mixed-integer programming problems, and we report the insights from our computational studies.

show abstract

Linear lexicographic optimization

Cited by 89 publications

References 6 publications

Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and grassmannian packings

Robust measurement design for detecting sparse signals: Equiangular uniform tight frames and grassmannian packings

Characterizations of efficient solutions under polyhedrality assumptions

Mitigating Delays and Unfairness in Appointment Systems

Contact Info

Product

Resources

About