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In this article, constrained continuous and combinatorial vector optimization problems (VOPs) are considered in the setting of finite-dimensional Euclidean spaces. Equivalence results between constrained integer and continuous VOPs are established by virtue of that between a constrained VOP and its penalized problem. Finally, one of the established equivalences is applied to derive necessary optimality conditions for a constrained integer VOP. [ABSTRACT FROM AUTHOR]

In this paper, some necessary and sufficient optimality conditions for the weakly efficient solutions of vector optimization problems (VOP) with finite equality and inequality constraints are shown by using two kinds of constraints qualifications in terms of the MP subdifferential due to Ye. A partial calmness and a penalized problem for the (VOP) are introduced and then the equivalence between the weakly efficient solution of the (VOP) and the local minimum solution of its penalized problem is proved under the assumption of partial calmness. [ABSTRACT FROM AUTHOR]

In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of feasible set for an equilibrium problem with a convex cone and generalize the notion of a Z-function for bifunctions. Under suitable assumptions, we derive some equivalence results of equilibrium problems, least element problems, and nonlinear programming problems. The results presented extend some results of [Riddell, R.C.: Equivalence of nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6, 462—474 (1981)] to equilibrium problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss the feasibility and solvability of vector complementarity problems. We prove that, under suitable conditions, the vector complementarity problem with a pseudomonotonicity assumption is solvable whenever it is strictly feasible. By strengthening the generalized monotonicity condition, we show also that the homogeneous vector complementarity problem is solvable whenever it is feasible. At last, we study the solvability of the vector complementarity problem on product spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two classes of variational-like inequalities with generalized monotone mappings in Banach spaces. Using the KKM technique, we obtain the existence of solutions for variational-like inequalities with relaxed η-α monotone mappings in reflexive Banach spaces. We present also the solvability of variational- like inequalities with relaxed η-α semimonotone mappings in arbitrary Banach spaces by means of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve the corresponding results of Refs. 1-6. [ABSTRACT FROM AUTHOR]

Blockade of fatty acid synthase (FASN), a key enzyme involved in de novo lipogenesis, results in robust death of ovarian cancer cells. However, known FASN inhibitors have proven to be poor therapeutic agents due to their ability to induce cachexia. Therefore, we sought to identify additional targets in the pathway linking FASN inhibition and cell death whose modulation might kill ovarian cancer cells without the attendant side effects. Here, we show that the initiator caspase-2 is required for robust death of ovarian cancer cells induced by FASN inhibitors. REDD1 (also known as Rtp801 or DDIT4), a known mTOR inhibitor previously implicated in the response to FASN inhibition, is a novel caspase-2 regulator in this pathway. REDD1 induction is compromised in ovarian cancer cells that do not respond to FASN inhibition. Inhibition of FASN induced an ATF4-dependent transcriptional induction of REDD1; downregulation of REDD1 prevented orlistat-induced activation of caspase-2, as monitored by its cleavage, proteolytic activity and dimerization. Abrogation of REDD1-mediated suppression of mTOR by TSC2 RNAi protected FASN inhibitor-sensitive ovarian cancer cells (OVCA420 cells) from orlistat-induced death. Conversely, suppression of mTOR with the chemical inhibitors PP242 or rapamycin-sensitized DOV13, an ovarian cancer cell line incapable of inducing REDD1, to orlistat-induced cell death through caspase-2. These findings indicate that REDD1 positively controls caspase-2-dependent cell death of ovarian cancer cells by inhibiting mTOR, placing mTOR as a novel upstream regulator of caspase-2 and supporting the possibility of manipulating mTOR to enhance caspase-2 activation in ovarian cancer. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of wellposedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-wellposedness is closely related to property (H). [ABSTRACT FROM AUTHOR]