相关论文: Convex Optimization in Julia

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…

We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…

For many applications, we need to use techniques to represent convex shapes and objects. In this work, we use level set method to represent shapes and find a necessary and sufficient condition on the level set function to guarantee the…

This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…

Motivated by the fact that not all nonconvex optimization problems are difficult to solve, we survey in this paper three widely-used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.…

Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…

This paper is motivated by the limit load, limit analysis and shear strength reduction methods, which are commonly employed in geotechnical stability analysis or similar applications. The aim is to make these methods more approachable by…

Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…

This thesis proposes an advanced, generic and high-level code rewriting and analysis system in the Julia programming language, providing applied equality saturation in the presence of multiple dispatch and metaprogramming. We show how our…

We focus on establishing the foundational paradigm of a novel optimization theory based on convolution with convex kernels. Our goal is to devise a morally deterministic model of locating the global optima of an arbitrary function, which is…

A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…

Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. It features a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…

Signal temporal logic (STL) is a powerful formalism for specifying various temporal properties in dynamical systems. However, existing methods, such as mixed-integer programming and nonlinear programming, often struggle to efficiently solve…

We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…

Control of complex systems involves both system identification and controller design. Deep neural networks have proven to be successful in many identification tasks, however, from model-based control perspective, these networks are…

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…