相关论文: Convex Optimization in Julia

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and…

This paper proposes a convex optimization based method that either locates all real roots of a set of power flow equations or declares no real solution exists in the given area. In the proposed method, solving the power flow equations is…

The scale of modern datasets necessitates the development of efficient distributed optimization methods for machine learning. We present a general-purpose framework for distributed computing environments, CoCoA, that has an efficient…

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…

Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic…

A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low…

This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…

A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…

This paper presents a novel methodology for solving the time-optimal trajectory optimization problem for interplanetary solar-sail missions using successive convex programming. Based on the non-convex problem, different convexification…

This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal…

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…

In this work, we study contextual strongly convex simulation optimization and adopt an "optimize then predict" (OTP) approach for real-time decision making. In the offline stage, simulation optimization is conducted across a set of…

In emerging scientific computing environments, matrix computations of increasing size and complexity are increasingly becoming prevalent. However, contemporary matrix language implementations are insufficient in their support for efficient…

This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…

Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…

Multiview representation learning is very popular for latent factor analysis. It naturally arises in many data analysis, machine learning, and information retrieval applications to model dependent structures among multiple data sources. For…