Related papers: A Constraint-Reduced MPC Algorithm for Convex Quad…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
Optimization-based controllers, such as Model Predictive Control (MPC), have attracted significant research interest due to their intuitive concept, constraint handling capabilities, and natural application to multi-input multi-output…
Nonlinear dynamics and safety constraints typically result in a nonlinear programming problem when applying model predictive control to achieve safe output consensus. To avoid the heavy computational burden of solving a nonlinear…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
Convolutional neural networks have shown tremendous performance capabilities in computer vision tasks, but their excessive amounts of weight storage and arithmetic operations prevent them from being adopted in embedded environments. One of…
Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
For networks of systems, with possibly improper transfer function matrices, we present a design framework which enables $\mathcal{H}_\infty$ control, while imposing sparsity constraints on the controller's coprime factors. We propose a…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…