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We develop a first-order (pseudo-)gradient approach for optimizing functions over the stationary distribution of discrete-time Markov chains (DTMC). We give insights into why solving this optimization problem is challenging and show how…
Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…
Large-scale non-convex optimization problems are expensive to solve due to computational and memory costs. To reduce the costs, first-order (computationally efficient) and asynchronous-parallel (memory efficient) algorithms are necessary to…
Embedding image features into a binary Hamming space can improve both the speed and accuracy of large-scale query-by-example image retrieval systems. Supervised hashing aims to map the original features to compact binary codes in a manner…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
The rapid adoption of deep learning has increasingly led to data-driven models replacing classical model-based algorithms, even in domains governed by well-understood physical laws. While data-driven models, such as long short-term memory…
Twin support vector machine~(TSVM) is a powerful learning algorithm by solving a pair of smaller SVM-type problems. However, there are still some specific issues such as low efficiency and weak robustness when it is faced with some real…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
We study the computational complexity of the non-preemptive scheduling problem of a list of independent jobs on a set of identical parallel processors with a makespan minimization objective. We make a maiden attempt to explore the…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
In this article we consider the problem of testing, for two finite sets of points in the Euclidean space, if their convex hulls are disjoint and computing an optimal supporting hyperplane if so. This is a fundamental problem of…
In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…
This paper shows that the OSGA algorithm -- which uses first-order information to solve convex optimization problems with optimal complexity -- can be used to efficiently solve arbitrary bound-constrained convex optimization problems. This…
A small improvement in the structure of the material could save the manufactory a lot of money. The free material design can be formulated as an optimization problem. However, due to its large scale, second-order methods cannot solve the…
In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent ("S"-inkhorn) and proximal gradient descent…
In this paper, we develop a new asymmetric framework for solving primal-dual problems of Conic Optimization by Interior-Point Methods (IPMs). It allows development of efficient methods for problems, where the dual formulation is simpler…
The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…
Nonlinear Convex Cone Programming (NCCP) problems are important and have many practical applications. In this paper, we introduces a flexible first-order primal-dual algorithm called the Variant Auxiliary Problem Principle (VAPP) for…
We study the problem of multiclass classification for settings where data features $\mathbf{x}$ and their labels $\mathbf{y}$ are uncertain. We identify that distributionally robust one-vs-all (OVA) classifiers often struggle in settings…
This paper studies Stochastic Shortest Path (SSP) problems in known and unknown environments from the perspective of convex optimisation. It first recalls results in the known parameter case, and develops understanding through different…