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

Intra-species genomic variation in the pine pathogen Fusarium circinatum

Fusarium circinatum is an important global pathogen of pine trees. Genome plasticity has been observed in different isolates of the fungus, but no genome comparisons are available. To address this gap, we sequenced and assembled to chromosome level five isolates of F. circinatum. These genomes were analysed together with previously published genomes of F. circinatum isolates, FSP34 and KS17. Multi-sample variant calling identified a total of 461,683 micro variants (SNPs and small indels) and a total of 1828 macro structural variants of which 1717 were copy number variants and 111 were inversions. The variant density was higher on the sub-telomeric regions of chromosomes. Variant annotation revealed that genes involved in transcription, transport, metabolism and transmembrane proteins were overrepresented in gene sets that were affected by high impact variants. A core genome representing genomic elements that were conserved in all the isolates and a non-redundant pangenome representing all genomic elements is presented. Whole genome alignments showed that an average of 93% of the genomic elements were present in all isolates. The results of this study reveal that some genomic elements are not conserved within the isolates and some variants are high impact. The described genome-scale variations will help to inform novel disease management strategies against the pathogen.DATA AVAILABILTY STATEMENT : The Whole Genome Shotgun project for Fusarium circinatum CMWF1803 has been deposited at DDBJ/ENA/GenBank under the accession JAEHFH000000000. The version described in this paper is version JAEHFH010000000. The Whole Genome Shotgun project for Fusarium circinatum CMWF560 has been deposited at DDBJ/ENA/GenBank under the accession JAEHFI000000000. The version described in this paper is version JAEHFI010000000. The Whole Genome Shotgun project for Fusarium circinatum CMWF567 has been deposited at DDBJ/ENA/GenBank under the accession JADZLS000000000. The version described in this paper is version JADZLS010000000. The Whole Genome Shotgun project for Fusarium circinatum UG27 has been deposited at DDBJ/ENA/ GenBank under the accession JAELVK000000000. The version described in this paper is version JAELVK010000000. The Whole Genome Shotgun project for Fusarium circinatum UG10 has been deposited at DDBJ/ENA/GenBank under the accession JAGJRQ000000000. The version described in this paper is version JAGJRQ010000000.The South African Department of Science and Innovation’s South African Research Chair Initiative and the DSI-NRF Centre of Excellence in Plant Health Biotechnology at the Forestry and Agricultural Biotechnology Institute (FABI), University of Pretoria.http://www.mdpi.com/journal/jofBiochemistryForestry and Agricultural Biotechnology Institute (FABI)GeneticsMicrobiology and Plant Patholog

Fritz-John Type Necessary Conditions for Optimality of Convex Generalized Semi-Infinite Optimization Problems

In this paper, we consider the Abadie and the Basic constraint qualifications (CQ) for lower level problem of convex generalized semi-infinite programming problems, and we derive the Fritz-John necessary optimality conditions for the problem under these constraint qualification

Two Constraint Qualifications for Non-Differentiable Semi-Infinite Programming Problems Using Fr´echet and Mordukhovich Subdifferentials

. In this paper, we consider the semi-infinite programming problems with non-differentiable emerging functions. Firstly, we give a counterexample showing that Theorem 3.1 of Ref. [10] is not true. Then, by modifying the assumptions of this theorem, we establish a new necessary Theorem for optimal solution of the problem

Karush-Kuhn-Tucker Types Optimality Conditions for Non-Smooth Semi-Infinite Vector Optimization Problems

In this paper we establish necessary and sufficient optimality conditions for a nondifferenriable, nonconvex semi-infinite vector optimization problem involving locally Lipschitz functions, whose constraints are required to depend continuously on an index j belonging to a compact set

Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems

This paper is devoted to the study of nonsmooth generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be locally Lipschitz. We introduce a constraint qualification which is based on the Mordukhovich subdifferential. Then, we derive a Fritz-John type necessary optimality condition. Finally, interrelations between the new and the existing constraint qualifications such as the Mangasarian-Fromovitz, linear independent, and the Slater are investigated.Generalized semi-infinite programming Mordukhovich subdifferential Constraint qualification Lagrangian Optimality condition Nonsmooth optimization