In a Hilbert setting, we introduce a new dynamic system and associated algorithms aimed at solving by rapid methods, monotone inclusions. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I + \lambda(t) {A})^{-1}$, where, in the resolvent, the positive control parameter $\lambda(t)$ tends to infinity as $t … Read more
Every local minimizer of a smooth constrained optimization problem satisfies the sequential Approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications … Read more
The increasing frequency of destructive wild land fires, with a consequent loss of life and property, has led to fire and land management agencies initiating extensive fuel management programs. This involves long-term scheduling of the location of fuel reduction activities such as prescribed burning or mechanical clearing. In this paper a Mixed Integer Programming (MIP) … Read more
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when the blocks are chosen in a cyclic order. A global sublinear rate of convergence is established … Read more
In this paper we mainly focus on optimization of sums of squares of quadratic functions, which we refer to as second-order least-squares problems, subject to convex constraints. Our motivation arises from applications in risk parity portfolio selection. We generalize the setting further by considering a class of nonlinear, non convex functions which admit a (non … Read more
In this paper we propose a corrected semi-proximal ADMM (alternating direction method of multipliers) for the general $p$-block $(p\!\ge 3)$ convex optimization problems with linear constraints, aiming to resolve the dilemma that almost all the existing modified versions of the directly extended ADMM, although with convergent guarantee, often perform substantially worse than the directly extended … Read more
This is a partial account of the fascinating history of Distance Geometry. We make no claim to completeness, but we do promise a dazzling display of beautiful, elementary mathematics. We prove Heron’s formula, Cauchy’s theorem on the rigidity of polyhedra, Cayley’s generalization of Heron’s formula to higher dimensions, Menger’s characterization of abstract semi-metric spaces, a … Read more
We investigate the multi-dimensional Super Resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the l1-minimization in the space of Radon measures in the multi-dimensional frame on semi-algebraic sets. While standard approaches have focused on SDP relaxations of the dual … Read more
The European emissions trading scheme (EU-ETS) is a cap and trade system that requires the indus- tries participating in the program to obtain allowances to cover their carbon emissions. Energy Intensive Industries claim that this system puts their European plants at an economics disadvantage compared to fa- cilities located outside the EU. As a direct … Read more
In this paper, we combine ideas from machine learning (ML) and operations research and management science (OR/MS) in developing a framework, along with specific methods, for using data to prescribe optimal decisions in OR/MS problems. In a departure from other work on data-driven optimization and reflecting our practical experience with the data available in applications … Read more