Related papers: First-order Methods for Unconstrained Vector Optim…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
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…
We introduce a novel approach for analyzing the performance of first-order black-box optimization methods. We focus on smooth unconstrained convex minimization over the Euclidean space $R^d$. Our approach relies on the observation that by…
Portfolio optimisation is a multi-objective optimisation problem (MOP), where an investor aims to optimise the conflicting criteria of maximising a portfolio's expected return whilst minimising its risk and other costs. However, selecting a…
In the framework of real Hilbert spaces we study continuous in time dynamics as well as numerical algorithms for the problem of approaching the set of zeros of a single-valued monotone and continuous operator $V$. The starting poin is a…
Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…
This article addresses the problem of derivative-free (single- or multi-objective) optimization subject to multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, non-linear and expensive to…
First-order methods (FOMs) have recently been applied and analyzed for solving problems with complicated functional constraints. Existing works show that FOMs for functional constrained problems have lower-order convergence rates than those…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
In this paper we combine the stochastic variance reduced gradient (SVRG) method [17] with the primal dual fixed point method (PDFP) proposed in [7] to solve a sum of two convex functions and one of which is linearly composite. This type of…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential applications in risk-averse machine learning, semisupervised learning, and robust optimization…
Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…
We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…