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As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
In this paper, we study the convergence properties of an iterative algorithm for fast nonlinear model predictive control of quasi-linear parameter-varying systems without inequality constraints. Compared to previous works considering this…
Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
Nonlinear robust optimization (NRO) is widely used in different applications, including energy, control, and economics, to make robust decisions under uncertainty. One of the classical solution methods in NRO is an outer approximation…
Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…
In this paper, we propose algorithms that exploit negative curvature for solving noisy nonlinear nonconvex unconstrained optimization problems. We consider both deterministic and stochastic inexact settings, and develop two-step algorithms…
We consider a property of positive polynomials on a compact set with a small perturbation. When applied to a Polynomial Optimization Problem (POP), the property implies that the optimal value of the corresponding SemiDefinite Programming…
Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
Convex relaxations of non-convex optimal power flow (OPF) problems have recently attracted significant interest. While existing relaxations globally solve many OPF problems, there are practical problems for which existing relaxations fail…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…