Generalizations of nondifferentiable convex functions and some characterizations

In this paper we generalize the convex functions, defining the concept of preconvex function and we study some characterizations by intervals, some characterizations by polytopes, some characterizations by level sets, some properties of the extreme points and some relations whith the convex functions. Also, we define the R-quasiconvex functions as a generalization of the quasiconvex functions, and we study some characterizations by level sets and by separation sets, and some relations with the quasiconvex functions

Semi-infinite interval equilibrium problems: optimality conditions and existence results

This paper aims to obtain new Karush–Kuhn–Tucker optimality conditions for solutions to semi-infinite interval equilibrium problems with interval-valued objective functions. The Karush–Kuhn–Tucker conditions for the semi-infinite interval programming problem are particular cases of those found in this paper for constrained equilibrium problem.We illustrate this with some examples. In addition, we obtain solutions to the interval equilibrium problem in the unconstrained case. The results presented in this paper extend the corresponding results in the literature.The research has been supported by FEDER Andalucía 2014-2020 (UPO-1381297) and by MICIN through grant MCIN/AEI/PID2021-123051NB-100

Second-order optimality conditions for interval-valued functions

This work is included in the search of optimality conditions for solutions to the scalar interval optimization problem, both constrained and unconstrained, by means of second-order optimality conditions. As it is known, these conditions allow us to reject some candidates to minima that arise from the first-order conditions. We will define new concepts such as second-order gH-derivative for interval-valued functions, 2-critical points, and 2-KKT-critical points. We obtain and present new types of interval-valued functions, such as 2-pseudoinvex, characterized by the property that all their second-order stationary points are global minima. We extend the optimality criteria to the semi-infinite programming problem and obtain duality theorems. These results represent an improvement in the treatment of optimization problems with interval-valued functions.Funding for open access publishing: Universidad de Cádiz/CBUA. The research has been supported by MCIN through grant MCIN/AEI/PID2021-123051NB-I00

Pareto optimality conditions and duality for vector quadratic fractional optimization problems

One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.Coordenação de aperfeiçoamento de pessoal de nivel superior (Brasil)Ministerio de Ciencia y TecnologíaConselho Nacional de Desenvolvimento Científico e Tecnológico (Brasil)Fundação de Amparo à Pesquisa do Estado de São Paul

A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions

Expression of P-glycoprotein and metallothionein in gastrointestinal stromal tumor and leiomyosarcomas. Clinical implications

We investigated the expression of P-glycoprotein (P-GP) and metallothionein (MT) in a series of 92 GIST and 14 gastrointestinal leiomyosarcomas (GILMS) with the purpose to expand our knowledge on the biological bases of GIST chemo-resistance and to ascertain their significance in patients’ prognosis. P-GP expression was more frequent in GIST than in GI-LMS (83.7% vs. 21.4%, p<0.001), with no difference between low- and high-risk GIST (p=1.000) or low- and high-grade GI-LMS (p=0.538). P-GP expression was unrelated to anatomic location (gastric vs. intestinal) in GIST (39/45 vs. 35/43, p=0.770) and in GI-LMS (0/2 vs. 2/6, p=1.000). MT expression was non-significantly higher in GI-LMS than in GIST (35.7% vs. 14.1%, p=0.060), with no difference between low- and high-risk GIST (p=1.000) or low- and high-grade GI-LMS (p=1.000). MT expression was unrelated to the anatomic location (gastric vs. intestinal) in GIST (7/45 vs. 6/43) and GI-LMS (0/2 vs. 1/6) (p=1.000 and p=0.1000, respectively). Overall tumor-specific survival (p< 0.001) and disease-free survival (p<0.001) were different in GIST as compared with GI-LMS, and the number of events was higher in GI-LMS. When the survival analysis took into consideration P-GP or MT expression, the overall survival in GIST was influenced by the expression of MT (p=0.021) but not by that of P-GP (p=0.638). However, in GI-LMS, P-GP expression influenced disease-free survival (p=0.050); in addition, it is important to recognize the limited value of these results because of the low number of cases involved in the study. Differential expression of P-GP and MT might explain the known variability in response to systemic chemotherapy in these tumors. Detection of P-GP and MT seems to add certain prognostic value in GIST (MT) or GI-LMS (P-GP)

Analysis of the mutational landscape of classic Hodgkin lymphoma identifies disease heterogeneity and potential therapeutic targets

Defining the mutational landscape of classic Hodgkin lymphoma is still a major research goal. New targeted next-generation sequencing (NGS) techniques may identify pathogenic mechanisms and new therapeutic opportunities related to this disease. We describe the mutational profile of a series of 57 cHL cases, enriched in Hodgkin and Reed-Sternberg (HRS) cells. Overall, the results confirm the presence of strong genomic heterogeneity. However, several variants were consistently detected in genes related to relevant signaling pathways, such as GM-CSF/IL-3, CBP/EP300, JAK/STAT, NF-kappaB, and numerous variants of genes affecting the B-cell receptor (BCR) pathway, such as BTK, CARD11, BCL10, among others. This unexpectedly high prevalence of mutations affecting the BCR pathway suggests some requirement for active BCR signaling for cHL cell viability. Additionally, incubation of a panel of cHL cellular models with selective BTK inhibitors in vitro constrains cell proliferation and causes cell death. Our results indicate new pathogenic mechanisms and therapeutic opportunities in this disease

Efficacy of naloxegol on symptoms and quality of life related to opioid-induced constipation in patients with cancer: a 3-month follow-up analysis

Objectives: Opioid-induced constipation (OIC) can affect up to 63% of all patients with cancer. The objectives of this study were to assess quality of life as well as efficacy and safety of naloxegol, in patients with cancer with OIC. Methods: An observational study was made of a cohort of patients with cancer and with OIC exhibiting an inadequate response to laxatives and treated with naloxegol. The sample consisted of adult outpatients with a Karnofsky performance status score ≥50. The Patient Assessment of Constipation Quality of Life Questionnaire (PAC-QOL) and the Patient Assessment of Constipation Symptoms (PAC-SYM) were applied for 3 months. Results: A total of 126 patients (58.2% males) with a mean age of 61.3 years (range 34-89) were included. Clinically relevant improvements (>0.5 points) were recorded in the PAC-QOL and PAC-SYM questionnaires (p<0.0001) from 15 days of treatment. The number of days a week with complete spontaneous bowel movements increased significantly (p<0.0001) from 2.4 to 4.6 on day 15, 4.7 after 1 month and 5 after 3 months. Pain control significantly improved (p<0.0001) during follow-up. A total of 13.5% of the patients (17/126) presented some gastrointestinal adverse reaction, mostly of mild (62.5%) or moderate intensity (25%). Conclusions: Clinically relevant improvements in OIC-related quality of life, number of bowel movements and constipation-related symptoms were recorded as early as after 15 days of treatment with naloxegol in patients with cancer and OIC, with a good safety profile