相关论文: Guaranteed Accuracy for Conic Programming Problems…
We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…
First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial programs in the face of data uncertainty. The class of convex programs, called robust SOS-convex programs, includes…
In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We propose a tube-based guaranteed cost model predictive controller considering a homothetic formulation for constrained linear systems subject to multiplicative structured norm-bounded uncertainties. It provides an upper bound to the…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
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…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
This paper examines the feasible region of a standard conic program represented as the intersection of a closed convex cone and a set of linear equalities. It is recently shown that when Slater constraint qualification (strict feasibility)…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…