Steepest descent method using novel adaptive stepsizes for unconstrained nonlinear multiobjective programming

Categories Convex Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

We propose new adaptive strategies to compute stepsizes for the steepest descent method to solve unconstrained nonlinear multiobjective optimization problems without employing any linesearch procedure. The resulting algorithms can be applied to a wide class of nonconvex unconstrained multi-criteria optimization problems satisfying a global Lipschitz continuity condition imposed on the gradients of all objectives. In … Read more

A Symmetric Primal-Dual method with two extrapolation steps for Composite Convex Optimization

Categories Convex Optimization Tags , , ,

Symmetry is a recurring feature in algorithms for monotone operator theory and convex optimization, particularly in problems involving the sum of two operators, as exemplified by the Peaceman–Rachford splitting scheme. However, in more general settings—such as composite optimization problems with three convex functions or structured convex-concave saddle-point formulations—existing algorithms often exhibit inherent asymmetry. In particular, … Read more

A surplus-maximizing two-sided multi-period non-convex ISO auction market

Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Other Topics Tags , , ,

Since the inception of ISOs, Locational Marginal Prices (LMPs) alone were not market clearing or incentive compatible because an auction winner who offered its avoidable costs could lose money at the LMPs. ISOs used make-whole payments to ensure that market participants did not lose money. Make-whole payments were not public, creating transparency issues. Over time, … Read more

Responsible Machine Learning via Mixed-Integer Optimization

Categories Applications - OR and Management Sciences, Integer Programming, Optimization in Data Science Tags , , , , , ,

In the last few decades, Machine Learning (ML) has achieved significant success across domains ranging from healthcare, sustainability, and the social sciences, to criminal justice and finance. But its deployment in increasingly sophisticated, critical, and sensitive areas affecting individuals, the groups they belong to, and society as a whole raises critical concerns around fairness, transparency … Read more

Alternating Methods for Large-Scale AC Optimal Power Flow with Unit Commitment

Categories (Mixed) Integer Nonlinear Programming, Energy Tags , , ,

Security-constrained unit commitment with alternating current optimal power flow (SCUC-ACOPF) is a central problem in power grid operations that optimizes commitment and dispatch of generators under a physically accurate power transmission model while encouraging robustness against component failures.  SCUC-ACOPF requires solving large-scale problems that involve multiple time periods and networks with thousands of buses within … Read more

Fast Stochastic Second-Order Adagrad for Nonconvex Bound-Constrained Optimization

Categories Bound-constrained Optimization, Data Science Algorithms, Nonlinear Optimization Tags , , , , , ,

ADAGB2, a generalization of the Adagrad algorithm for stochastic optimization is introduced, which is also applicable to bound-constrained problems and capable of using second-order information when available. It is shown that, given  delta in (0,1) and epsilon in (0,1], the ADAGB2 algorithm needs at most O(epsilon^{-2}) iterations to ensure an epsilon-approximate first-order critical point of … Read more

A Practical GPU-Enhanced Matrix-Free Primal-Dual Method for Large-Scale Conic Programs

Categories Cone Programming, Linear, Cone and Semidefinite Programming, Second-Order Cone Programming

In this paper, we introduce a practical GPU-enhanced matrix-free first-order method for solving large-scale conic programming problems, which we refer to as PDCS, standing for the Primal-Dual Conic Programming Solver. Problems that it solves include linear programs, second-order cone programs, convex quadratic programs, and exponential cone programs. The method avoids matrix factorizations and uses sparse … Read more

A Graphical Global Optimization Framework for Parameter Estimation of Statistical Models with Nonconvex Regularization Functions

Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Global Optimization Theory Tags , , , ,

Optimization problems with norm-bounding constraints appear in various applications, from portfolio optimization to machine learning, feature selection, and beyond. A widely used variant of these problems relaxes the norm-bounding constraint through Lagrangian relaxation and moves it to the objective function as a form of penalty or regularization term. A challenging class of these models uses … Read more

A Fast Newton Method Under Local Lipschitz Smoothness

Categories Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

A new, fast second-order method is proposed that achieves the optimal \(\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right) \) complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the standard global Lipschitz Hessian continuity condition, but onlyusing an appropriate local smoothness requirement. The algorithm exploits Hessian information to compute a Newton step and a negative curvature step when … Read more

An Adaptive Stochastic Dual Progressive Hedging Algorithm for Stochastic Programming

Categories Stochastic Approaches, Stochastic Programming Tags , , ,

The Progressive Hedging (PH) algorithm is one of the cornerstones in large-scale stochastic programming. However, its traditional development requires that all scenario subproblems are solved per iteration, and a probability distribution with finitely many outcomes. This paper introduces a stochastic dual PH algorithm (SDPH) to overcome these challenges. We introduce an adaptive sampling process and … Read more