Optimality conditions in convex multiobjective SIP

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P

Interactions Between Laminin Receptor and the Cytoskeleton During Translation and Cell Motility

Human laminin receptor acts as both a component of the 40S ribosomal subunit to mediate cellular translation and as a cell surface receptor that interacts with components of the extracellular matrix. Due to its role as the cell surface receptor for several viruses and its overexpression in several types of cancer, laminin receptor is a pathologically significant protein. Previous studies have determined that ribosomes are associated with components of the cytoskeleton, however the specific ribosomal component(s) responsible has not been determined. Our studies show that laminin receptor binds directly to tubulin. Through the use of siRNA and cytoskeletal inhibitors we demonstrate that laminin receptor acts as a tethering protein, holding the ribosome to tubulin, which is integral to cellular translation. Our studies also show that laminin receptor is capable of binding directly to actin. Through the use of siRNA and cytoskeletal inhibitors we have shown that this laminin receptor-actin interaction is critical for cell migration. These data indicate that interactions between laminin receptor and the cytoskeleton are vital in mediating two processes that are intimately linked to cancer, cellular translation and migration

Evidence for a retroviral insertion in TRPM1 as the cause of congenital stationary night blindness and leopard complex spotting in the horse

Leopard complex spotting is a group of white spotting patterns in horses caused by an incompletely dominant gene (LP) where homozygotes (LP/LP) are also affected with congenital stationary night blindness. Previous studies implicated Transient Receptor Potential Cation Channel, Subfamily M, Member 1 (TRPM1) as the best candidate gene for both CSNB and LP. RNA-Seq data pinpointed a 1378 bp insertion in intron 1 of TRPM1 as the potential cause. This insertion, a long terminal repeat (LTR) of an endogenous retrovirus, was completely associated with LP, testing 511 horses (χ²=1022.00, p<<0.0005), and CSNB, testing 43 horses (χ2=43, p<<0.0005). The LTR was shown to disrupt TRPM1 transcription by premature poly-adenylation. Furthermore, while deleterious transposable element insertions should be quickly selected against the identification of this insertion in three ancient DNA samples suggests it has been maintained in the horse gene pool for at least 17,000 years. This study represents the first description of an LTR insertion being associated with both a pigmentation phenotype and an eye disorder.Rebecca R. Bellone … David L. Adelson, Sim Lin Lim … et al

Nondifferentiable fractional semi-infinite multiobjective optimization problems

Employing some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for local (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with an infinite number of inequality constraints. Sufficient conditions for such solutions to the considered problem are also obtained by means of proposing the use of (strictly) generalized convex functions. In addition, we state a dual problem to the primal one and explore duality relations

Robust second order cone conditions and duality for multiobjective problems under uncertainty data

This paper studies a class of multiobjective convex polynomial problems, where both the constraint and objective functions involve uncertain parameters that reside in ellipsoidal uncertainty sets. Employing the robust deterministic approach, we provide necessary conditions and sufficient conditions, which are exhibited in relation to second order cone conditions, for robust (weak) Pareto solutions of the uncertain multiobjective optimization problem. A dual multiobjective problem is proposed to examine robust converse, robust weak and robust strong duality relations between the primal and dual problems. Moreover, we establish robust solution relationships between the uncertain multiobjective optimization program and a (scalar) second order cone programming relaxation problem of a corresponding weighted-sum optimization problem. This in particular shows that we can find a robust (weak) Pareto solution of the uncertain multiobjective optimization problem by solving a second order cone programming relaxation.Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2024-26-01

An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs

We present an exact formula for the radius of robust feasibility of uncertain linear programs with a compact and convex uncertainty set. The radius of robust feasibility provides a value for the maximal ‘size’ of an uncertainty set under which robust feasibility of the uncertain linear program can be guaranteed. By considering spectrahedral uncertainty sets, we obtain numerically tractable radius formulas for commonly used uncertainty sets of robust optimization, such as ellipsoids, balls, polytopes and boxes. In these cases, we show that the radius of robust feasibility can be found by solving a linearly constrained convex quadratic program or a minimax linear program. The results are illustrated by calculating the radius of robust feasibility of uncertain linear programs for several different uncertainty sets

Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems

The version of the article archived on this institutional repository is a pre-print. It has not been certified by peer review. The final versionis available online at: https://doi.org/10.1007/s10957-023-02197-1 .In this paper, we examine stable exact relaxations for classes of parametric robust convex polynomial optimization problems under affinely parameterized data uncertainty in the constraints. We first show that a parametric robust convex polynomial problem with convex compact uncertainty sets enjoys stable exact conic relaxations under the validation of a characteristic cone constraint qualification. We then show that such stable exact conic relaxations become stable exact semidefinite programming relaxations for a parametric robust SOS-convex polynomial problem, where the uncertainty sets are assumed to be bounded spectrahedra. In addition, under the corresponding constraint qualification, we derive stable exact second-order cone programming relaxations for some classes of parametric robust convex quadratic programs under ellipsoidal uncertainty sets.National Foundation for Science and Technology Development of Vietnam (NAFOSTED) under grant number 101.01 2020.09 (to TDC); Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22 (to JVP); Generalitat Valenciana, Grant AICO/2021/165 (to JVP)

Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets

In this paper, we study a robust optimization problem whose constraints include nonsmooth and nonconvex functions and the intersection of closed sets. Using advanced variational analysis tools, we first provide necessary conditions for the optimality of the robust optimization problem. We then establish sufficient conditions for the optimality of the considered problem under the assumption of generalized convexity. In addition, we present a dual problem to the primal robust optimization problem and examine duality relations.Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number T2024-26-01