相关论文: An Efficient Optimization Approach for a Cardinali…

We propose a new splitting and successively solving augmented Lagrangian (SSAL) method for solving an optimization problem with both semicontinuous variables and a cardinality constraint. This optimization problem arises in several contexts…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

Control design for robotic systems is complex and often requires solving an optimization to follow a trajectory accurately. Online optimization approaches like Model Predictive Control (MPC) have been shown to achieve great tracking…

This paper makes the Millennium Prize problem P vs NP operational in quantitative finance by studying cardinality-constrained portfolio selection. Starting from the convex Markowitz mean-variance program with CAPM-based expected returns (Rf…

Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal…

Integer variables allow the treatment of some portfolio optimization problems in a more realistic way and introduce the possibility of adding some natural features to the model. We propose an algebraic approach to maximize the expected…

This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk.…

We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware…

In decentralized optimization over networks, each node in the network has a portion of the global objective function and the aim is to collectively optimize this function. Gradient tracking methods have emerged as a popular alternative for…

Visual tracking is typically solved as a discriminative learning problem that usually requires high-quality samples for online model adaptation. It is a critical and challenging problem to evaluate the training samples collected from…

This paper is concerned with portfolio optimization models for creating high-quality lists of recommended items to balance the accuracy and diversity of recommendations. However, the statistics (i.e., expectation and covariance of ratings)…

Semi-supervised clustering problems focus on clustering data with labels. In this paper,we consider the semi-supervised hypergraph problems. We use the hypergraph related tensor to construct an orthogonal constrained optimization model. The…

This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…

In this paper, we study asset selection methods to construct a sparse index tracking portfolio. For its advantage over full replication portfolio, the concept of sparse index tracking portfolio has significant attention in the field of…

This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and inequality constraints, naturally arises in a wide range of engineering and machine learning applications.…

This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…

Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the…

In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…