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In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…
A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
Many real-world applications are characterized by a number of conflicting performance measures. As optimizing in a multi-objective setting leads to a set of non-dominated solutions, a preference function is required for selecting the…
In this article, we work with set-valued optimization problems in locally convex topological vector spaces. We prove the equivalencies of some definitions of generalized convex maps introduced by Jeyakumar, Yang, Yang & Yang & Chen, as well…
There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
In this paper, we develop a socially cooperative optimal control framework to address the motion planning problem for connected and automated vehicles (CAVs) in mixed traffic using social value orientation (SVO) and a potential game…
Multi-Objective Optimization (MOO) techniques have become increasingly popular in recent years due to their potential for solving real-world problems in various fields, such as logistics, finance, environmental management, and engineering.…
We consider the problem of constrained multi-objective blackbox optimization using expensive function evaluations, where the goal is to approximate the true Pareto set of solutions satisfying a set of constraints while minimizing the number…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
In this paper we consider the problem of optimization of approximate integration of set-valued functions from the class defined by given majorant of their moduli of continuity, using values of the functions at $n$ fixed or free points of…
Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
Consider a set of discounted optimal stopping problems for a one-parameter family of objective functions and a fixed diffusion process, started at a fixed point. A standard problem in stochastic control/optimal stopping is to solve for the…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
Many real-world problems require trading off multiple competing objectives. However, these objectives are often in different units and/or scales, which can make it challenging for practitioners to express numerical preferences over…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…