Convex relaxations of nonconvex functions are useful in methods for global optimization, since local minimization of a convex relaxation will provide a lower bound for the overarching global ...

├── index.html # Main landing page ├── css/ │ └── style.css # Responsive CSS styles ├── topics/ │ └── convexity.html # Understanding convexity page ├── images/ # Placeholder for future diagrams and ...

Abstract: This article is devoted to the distributed convex optimization problem for a class of nonlinear multiagent systems under set constraints. The optimization objective function is composed of ...

Abstract: This article presents a prediction-correction proximal method (PCPM) for the general nonsmooth convex optimization problem with linear equality and inequality constraints. The proposed ...

ABSTRACT: In this paper, we show that some functions related to the dual Simpson’s formula and Bullen- Simpson’s formula are Schur-convex provided that f is four-convex. These results should be ...

This course discusses basic convex analysis (convex sets, functions, and optimization problems), optimization theory (linear, quadratic, semidefinite, and geometric programming; optimality conditions ...

ABSTRACT: This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the ...