Related papers: A New Active Set Scheme for Quadratic Programing
A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We devise a new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure. More specifically, we introduce a new class of estimating functions, which are obtained by…
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. Within this framework, a quantum subroutine is incorporated…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We propose a combinatorial method for computing explicit solutions to multi-parametric quadratic programs, which can be used to compute explicit control laws for linear model predictive control. In contrast to classical methods, which are…
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
Active metric learning is the problem of incrementally selecting high-utility batches of training data (typically, ordered triplets) to annotate, in order to progressively improve a learned model of a metric over some input domain as…
Chance-constrained programming is a widely used framework for decision-making under uncertainty, yet its mixed-integer reformulations involve nonconvex mixing sets with a knapsack constraint, leading to weak relaxations and computational…
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that…
The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the…
Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…