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Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

The primal-dual hybrid gradient (PDHG) algorithm is popular in solving min-max problems which are being widely used in a variety of areas. To improve the applicability and efficiency of PDHG for different application scenarios, we focus on…

We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

We propose a novel dynamically weighted inertial forward-backward algorithm (DWIFOB) for solving structured monotone inclusion problems. The scheme exploits the globally convergent forward-backward algorithm with deviations in [26] as the…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

The super-sensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots -- phase values at which sensitivity is totally lost. One remedy is to use a…

We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient…

Inspired by the Optimistic Gradient Ascent-Proximal Point Algorithm (OGAProx) proposed by Bo{\c{t}}, Csetnek, and Sedlmayer for solving a saddle-point problem associated with a convex-concave function with a nonsmooth coupling function and…

Very recently proximal policy optimization (PPO) algorithms have been proposed as first-order optimization methods for effective reinforcement learning. While PPO is inspired by the same learning theory that justifies trust region policy…

The feedback alignment (FA) algorithm offers a biologically plausible alternative to backpropagation (BP) for training neural networks yet notably fails to scale to convolutional architectures. Modifications have been proposed to address…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…

This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized…

Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…