Related papers: An affine scaling method using a class of differen…
Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…
We introduce efficient differentially private (DP) algorithms for several linear algebraic tasks, including solving linear equalities over arbitrary fields, linear inequalities over the reals, and computing affine spans and convex hulls. As…
We develop a natural variant of Dikin's affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty…
Bi-level optimization model is able to capture a wide range of complex learning tasks with practical interest. Due to the witnessed efficiency in solving bi-level programs, gradient-based methods have gained popularity in the machine…
Feature engineering, a crucial step of machine learning, aims to extract useful features from raw data to improve data quality. In recent years, great efforts have been devoted to Automated Feature Engineering (AutoFE) to replace expensive…
Self-scaled barrier functions are fundamental objects in the theory of interior-point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self-scaled…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known…
Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques…
Strict linear feasibility or linear separation is usually tackled using efficient approximation/stochastic algorithms (that may even run in sub-linear times in expectation). However, today state of the art for solving…
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain…
This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using the more efficient online algorithms through time-varying optimization. The idea lies in that…
Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these…