Optimality and Duality for Multiobjective Fractional Programming Involvingn-Set Functions

AbstractWe consider a multiobjective fractional programming problem (MFP) involving vector-valued objectiven-set functions in which their numerators are different from each other, but their denominators are the same. By using the concept of proper efficiency, we establish optimality conditions and duality relations for our problem (MFP) under convexity assumptions on objective and constrained functions

Peroxisome Proliferators-Activated Receptor (PPAR) Modulators and Metabolic Disorders

Overweight and obesity lead to an increased risk for metabolic disorders such as impaired glucose regulation/insulin resistance, dyslipidemia, and hypertension. Several molecular drug targets with potential to prevent or treat metabolic disorders have been revealed. Interestingly, the activation of peroxisome proliferator-activated receptor (PPAR), which belongs to the nuclear receptor superfamily, has many beneficial clinical effects. PPAR directly modulates gene expression by binding to a specific ligand. All PPAR subtypes (α, γ, and σ) are involved in glucose metabolism, lipid metabolism, and energy balance. PPAR agonists play an important role in therapeutic aspects of metabolic disorders. However, undesired effects of the existing PPAR agonists have been reported. A great deal of recent research has focused on the discovery of new PPAR modulators with more beneficial effects and more safety without producing undesired side effects. Herein, we briefly review the roles of PPAR in metabolic disorders, the effects of PPAR modulators in metabolic disorders, and the technologies with which to discover new PPAR modulators