Related papers: Provably data-driven projection method for quadrat…
We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…
We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…
We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms.…
Random projection techniques based on Johnson-Lindenstrauss lemma are used for randomly aggregating the constraints or variables of optimization problems while approximately preserving their optimal values, that leads to smaller-scale…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
Quadratic programming (QP) underpins real-time robotics by enabling efficient, constrained optimization in state estimation, motion planning, and control. In legged locomotion and manipulation, essential modules like inverse dynamics, Model…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
The article presents a new method of linear programming, called the surface movement method. This method constructs an optimal objective path on the surface of the feasible polytope from the initial boundary point to the point at which 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…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
We propose a sequential quadratic programming (SQP) method that can incorporate adaptive sampling for stochastic nonsmooth nonconvex optimization problems with upper-C^2 objectives. Upper-$\Ctwo$ functions can be viewed as…
We study how much a linear program (LP) can be compressed when solved repeatedly, given prior knowledge about its objective function. Existing data-driven projection methods learn low-dimensional surrogate LPs with approximate…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…
Recently, a lot of attention has been devoted to finding physically realisable operations that realise as closely as possible certain desired transformations between quantum states, e.g. quantum cloning, teleportation, quantum gates, etc.…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…
In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve…
We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters.…