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The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk…
Optimization on the Stiefel manifold or with orthogonality constraints is an important problem in many signal processing and data analysis applications such as Sparse Principal Component Analysis (SPCA). Algorithms such as the Riemannian…
In recent years, the evaluation of the minimal investment risk of the quenched disordered system of a portfolio optimization problem and the investment concentration of the optimal portfolio has been actively investigated using the analysis…
Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
Value-at-Risk (VaR) is one of the main regulatory tools used for risk management purposes. However, it is difficult to compute optimal VaR portfolios; that is, an optimal risk-reward portfolio allocation using VaR as the risk measure. This…
This paper studies a variable proportion portfolio insurance (VPPI) strategy. The objective is to determine the risk multiplier by maximizing the extended Omega ratio of the investor's cushion, using a binary stochastic benchmark. When the…
In quantitative Magnetic Resonance Imaging, traditional methods suffer from the so-called Partial Volume Effect (PVE) due to spatial resolution limitations. As a consequence of PVE, the parameters of the voxels containing more than one…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem,…
In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Risk aversion plays a significant and central role in investors' decisions in the process of developing a portfolio. In this framework of portfolio optimization we determine the portfolio that possesses the minimal risk by using a new…
Portfolio optimization is a critical area in finance, aiming to maximize returns while minimizing risk. Metaheuristic algorithms were shown to solve complex optimization problems efficiently, with Genetic Algorithms and Particle Swarm…
We give algorithms for designing near-optimal sparse controllers using policy gradient with applications to control of systems corrupted by multiplicative noise, which is increasingly important in emerging complex dynamical networks.…