Related papers: A Second-Order Algorithm Based on Affine Scaling I…
While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted towards second-order stationary points…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
The Moment/Sum-of-squares hierarchy provides a way to compute the global minimizers of polynomial optimization problems (POP), at the cost of solving a sequence of increasingly large semidefinite programs (SDPs). We consider large-scale…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
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…
This paper addresses the problem of the optimal $H_2$ controller design for compartmental systems. In other words, we aim to enhance system robustness while maintaining the law of mass conservation. We perform a novel problem transformation…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network that can communicate with neighbors only. The proximal method of multipliers is…
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
Hyperbolic (HB) programming generalizes many popular convex optimization problems, including semidefinite and second-order cone programming. Despite substantial theoretical progress on HB programming, efficient computational tools for…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…