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Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...

Lipschitz modulus in convex semi-infinite optimization via d.c. functions

María J. Cánovas, Abderrahim Hantoute, Marco A. López, Juan Parra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem's data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...

Local Changes in Lipid Composition to Match Membrane Curvature

Rolf J. Ryham (2016)

Molecular Based Mathematical Biology

A continuum mechanical model based on the Helfrich Hamiltonian is devised to investigate the coupling between lipid composition and membrane curvature. Each monolayer in the bilayer is modeled as a freely deformable surface with a director field for lipid orientation. A scalar field for the mole fraction of two lipid types accounts for local changes in composition. It allows lipids to access monolayer regions favorable to their intrinsic curvature at the expense of increasing entropic free energy....

Local stability and differentiability of the Mean–Conditional Value at Risk model defined on the mixed–integer loss functions

Martin Branda (2010)

Kybernetika

In this paper, we study local stability of the mean-risk model with Conditional Value at Risk measure where the mixed-integer value function appears as a loss variable. This model has been recently introduced and studied in~Schulz and Tiedemann [16]. First, we generalize the qualitative results for the case with random technology matrix. We employ the contamination techniques to quantify a possible effect of changes in the underlying probability distribution on the optimal value. We use the generalized...

Locally bounded k-colorings of trees

C. Bentz, C. Picouleau (2009)

RAIRO - Operations Research

Given a tree T with n vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of T respecting local (i.e., associated with p prespecified subsets of vertices) color bounds can be solved in O(n6p-1logn) time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

Locally Lipschitz vector optimization with inequality and equality constraints

Ivan Ginchev, Angelo Guerraggio, Matteo Rocca (2010)

Applications of Mathematics

The present paper studies the following constrained vector optimization problem: min C f ( x ) , g ( x ) - K , h ( x ) = 0 , where f : n m , g : n p are locally Lipschitz functions, h : n q is C 1 function, and C m and K p are closed convex cones. Two types of solutions are important for the consideration, namely w -minimizers (weakly efficient points) and i -minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x 0 to be a w -minimizer and first-order sufficient conditions for x 0 ...

Managing a patient waiting list with time-dependent priority and adverse events

Daiki Min, Yuehwern Yih (2014)

RAIRO - Operations Research - Recherche Opérationnelle

This paper addresses the problem of managing a waiting list for elective surgery to decide the number of patients selected from the waiting list and to schedule them in accordance with the operating room capacity in the next period. The waiting list prioritizes patients not only by their initial urgency level but also by their waiting time. Selecting elective surgery patients requires a balance between the waiting time for urgent patients and that for less urgent patients. The problem is formulated...

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