相关论文: Multiobjective Balanced Gradient Flow: A Dynamical…
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…
Optimal Power Flow (OPF) can be modeled as a non-convex Quadratically Constrained Quadratic Program (QCQP). Our purpose is to solve OPF to global optimality. To this end, we specialize the Mixed-Integer Quadratic Convex Reformulation method…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
In numerous reinforcement learning (RL) problems involving safety-critical systems, a key challenge lies in balancing multiple objectives while simultaneously meeting all stringent safety constraints. To tackle this issue, we propose a…
Interpreting motion captured in image sequences is crucial for a wide range of computer vision applications. Typical estimation approaches include optical flow (OF), which approximates the apparent motion instantaneously in a scene, and…
Recommender systems need to mirror the complexity of the environment they are applied in. The more we know about what might benefit the user, the more objectives the recommender system has. In addition there may be multiple stakeholders -…
We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…
In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…
In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of the classical sub-gradient method to the setting of convex bi-level optimization problems. This is a first-order method that is very easy to…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
Multi-objective gradient methods are becoming the standard for solving multi-objective problems. Among others, they show promising results in developing multi-objective recommender systems with both correlated and conflicting objectives.…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…