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The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
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…
This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
This paper explores two condensed-space interior-point methods to efficiently solve large-scale nonlinear programs on graphics processing units (GPUs). The interior-point method solves a sequence of symmetric indefinite linear systems, or…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
In this paper, we introduce two parabolic target-space interior-point algorithms for solving monotone linear complementarity problems. The first algorithm is based on a universal tangent direction, which has been recently proposed for…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
We propose and analyse primal-dual interior-point algorithms for convex optimization problems in conic form. The families of algorithms we analyse are so-called short-step algorithms and they match the current best iteration complexity…
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…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We prove that the classic logarithmic barrier problem is equivalent to a particular logarithmic barrier positive relaxation problem with barrier and scaling parameters. Based on the equivalence, a line-search primal-dual interior-point…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…